JEE Main & Advanced Physics NLM, Friction, Circular Motion Question Bank

done Self Evaluation Test - Laws of Motion Total Questions - 100

• question_answer1)

  A mass of 1 kg is suspended by a thread. It is

  (i) lifted up with an acceleration \[4.9\text{ }m/{{s}^{2}}\],

  (ii) Lowered with an acceleration\[4.9\text{ }m/{{s}^{2}}\].

  The ratio of the tensions is

  A)
  \[3\text{ }:\text{ }1\] done clear
  B)
  \[1\text{ }:\text{ }2\]   done clear
  C)
  \[1\text{ }:\text{ }3\] done clear
  D)
  \[2\text{ }:\text{ }1\] done clear
  View Solution play_arrow

• question_answer2)
  A monkey is descending from the branch of a tree with constant acceleration. If the breaking strength is 75% of the weight of the monkey, the minimum acceleration with which monkey can slide down without breaking the branch is
  A)
  g   done clear
  B)
  \[\frac{3g}{4}\] done clear
  C)
  \[\frac{g}{4}\] done clear
  D)
  \[\frac{g}{2}\] done clear
  View Solution play_arrow

• question_answer3)
  In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4 m just after the system is released from rest is \[(\theta ={{\sin }^{-1}}3/5)\]
  A)
  \[\frac{2g}{5}\]downwards done clear
  B)
  \[\frac{2g}{5}\] upwards done clear
  C)
  \[\frac{5g}{11}\]downwards done clear
  D)
  \[\frac{5g}{11}\]upwards done clear
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• question_answer4)
  Two blocks A and B of masses 3 m and m respectively are connected by a massless and inextensible string. The whole system is suspended by massless spring as shown in figure.                             The magnitudes of acceleration of A and B immediately after the string is cut, are respectively:
  A)
  \[\frac{g}{3},g\]  done clear
  B)
  \[~g,\text{ }g\] done clear
  C)
  \[\frac{g}{3},\frac{g}{3}\]   done clear
  D)
  \[g,\frac{g}{3}\] done clear
  View Solution play_arrow

• question_answer5)
  One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed V the net force on the particle (directed towards center) will be (T represents the tension in the string)
  A)
  \[T+\frac{m{{v}^{2}}}{l}\] done clear
  B)
   \[T-\frac{m{{v}^{2}}}{l}\] done clear
  C)
   Zero  done clear
  D)
  T done clear
  View Solution play_arrow

• question_answer6)
  Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a motionless surface, as shown. If a force of 14 N is applied on the 4 kg block then the contact force between A
  A)
  6 N done clear
  B)
  8 N done clear
  C)
  18 N done clear
  D)
  2 N done clear
  View Solution play_arrow

• question_answer7)
    A balloon with mass 'm' is descending down with an acceleration 'a' (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration 'a'?
  A)
  \[\frac{2ma}{g+a}\]  done clear
  B)
  \[\frac{2ma}{g-a}\] done clear
  C)
  \[\frac{ma}{g+a}\] done clear
  D)
  \[\frac{ma}{g-a}\] done clear
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• question_answer8)
  A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car.  The car is moving with constant acceleration a directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration a vertically. The tension in the string is equal to               
  A)
  \[m\sqrt{{{g}^{2}}+{{a}^{2}}}\]   done clear
  B)
  \[m\sqrt{{{g}^{2}}+{{a}^{2}}}-ma\] done clear
  C)
  \[m\sqrt{{{g}^{2}}+{{a}^{2}}}+ma\]            done clear
  D)
  \[m\left( g+a \right)\] done clear
  View Solution play_arrow

• question_answer9)
  Five persons A, B, C, D and E are pulling a cart of mass 100 kg on a smooth surface and cart is moving with acceleration \[3\text{ }m/{{s}^{2}}\]in east direction. When person A stops pulling, it moves with acceleration \[1\text{ }m/{{s}^{2}}\]in the west direction. When person B stops pulling, it moves with acceleration \[\text{24 }m/{{s}^{2}}\] in the north direction. The magnitude of acceleration of the cart when only A and B pull the cart keeping their directions same as the old directions, is
  A)
  \[\text{24 }m/{{s}^{2}}\] done clear
  B)
  \[\text{3}\sqrt{71}\text{ }m/{{s}^{2}}\] done clear
  C)
  \[\text{30 }m/{{s}^{2}}\] done clear
  D)
  \[\text{25 }m/{{s}^{2}}\] done clear
  View Solution play_arrow

• question_answer10)
  A particle of mass 0.3 kg subject to a force \[F=-kx\] with\[k=15\text{ }N/m\]. What will be its initial acceleration if it is released from a point 20 cm away from the origin?
  A)
  \[15\text{ }m/{{s}^{2}}\]  done clear
  B)
  \[3\text{ }m/{{s}^{2}}\] done clear
  C)
  \[10\text{ }m/{{s}^{2}}\] done clear
  D)
  \[5\text{ }m/{{s}^{2}}\] done clear
  View Solution play_arrow

• question_answer11)
  If a stone is thrown out of an accelerated train, then acceleration of the stone at any instant depends on
  A)
  force acting on it at that instant done clear
  B)
  acceleration of the train done clear
  C)
  Both [a] & [b] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  A 600 kg rocket is set for a vertical firing. If the exhaust speed is \[1000\text{ }m{{s}^{-1}}\], the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is
  A)
  \[117.6\text{ kg}{{\text{s}}^{-1}}\] done clear
  B)
  \[58.6\text{ kg}{{\text{s}}^{-1}}\] done clear
  C)
  \[6\text{ kg}{{\text{s}}^{-1}}\]  done clear
  D)
  \[76.4\text{ kg}{{\text{s}}^{-1}}\] done clear
  View Solution play_arrow

• question_answer13)
  An object of mass 10 kg moves at a constant speed of\[10\text{ }m{{s}^{-1}}\]. A constant force that acts for 4 sec on the object gives it a speed of \[2\text{ }m{{s}^{-1}}\] in opposite direction. The force acting on the object is
  A)
  -3N done clear
  B)
  -30 N done clear
  C)
  3N done clear
  D)
  30 N done clear
  View Solution play_arrow

• question_answer14)
  A player stops a football weighting 0.5 kg which comes flying towards him with a velocity of 10m/ s. If the impact lasts for 1/50th sec. and the ball bounces back with a velocity of 15 m/s, then the average force involved is
  A)
  250 N done clear
  B)
  1250 N done clear
  C)
  500 N done clear
  D)
  625 N done clear
  View Solution play_arrow

• question_answer15)
  A truck accelerates on a horizontal road due to the force exerted by the
  A)
  road done clear
  B)
  engine done clear
  C)
  earth done clear
  D)
  driver done clear
  View Solution play_arrow

• question_answer16)
  A block of mass 4 kg is suspended through two light spring balances A and B. Then A and B will read respectively:
  A)
  4 kg and zero kg done clear
  B)
  Zero kg and 4 kg                done clear
  C)
  4 kg and 4 kg  done clear
  D)
  2 kg and 2 kg               done clear
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• question_answer17)
  A block of mass m is placed on a smooth wedge of inclination 6. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be
  A)
  \[mg/cos\,\theta \] done clear
  B)
  \[mg\text{ }cos\,\theta \] done clear
  C)
  \[mg\text{ sin}\,\theta \] done clear
  D)
  \[mg\] done clear
  View Solution play_arrow

• question_answer18)
  If n bullets each of mass m are fired with a velocity v per second from a machine gun, the force required to hold the gun in position is
  A)
  \[\left( n+1 \right)mv\] done clear
  B)
  \[\frac{mv}{{{n}^{2}}}\] done clear
  C)
  \[\frac{mv}{n}\] done clear
  D)
  \[mnv\] done clear
  View Solution play_arrow

• question_answer19)
  A ball of mass 10 g moving perpendicular to the plane of the wall strikes it and rebounds in the same line with the same velocity. If the impulse experienced by the wall is 0.54 Ns, the velocity of the ball is
  A)
  \[27\text{ }m{{s}^{-1}}\] done clear
  B)
  \[3.7\text{ }m{{s}^{-1}}\] done clear
  C)
  \[54\text{ }m{{s}^{-1}}\] done clear
  D)
  \[37\text{ }m{{s}^{-1}}\] done clear
  View Solution play_arrow

• question_answer20)
  Two bodies of masses 1 kg and 2 kg moving with same velocities are stopped by the same force. Then the ratio of their stopping distances is
  A)
  \[1:2\] done clear
  B)
  \[2:1\]   done clear
  C)
  (c)\[\sqrt{2}:1\] done clear
  D)
  \[1:\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer21)
  A hammer weighing 3 kg strikes the head of a nail with a speed of \[2\text{ }m{{s}^{-1}}\] drives it by 1 cm into the wall. The impulse imparted to the wall is
  A)
  6Ns done clear
  B)
  3Ns done clear
  C)
  2Ns done clear
  D)
  12 Ns done clear
  View Solution play_arrow

• question_answer22)
  The force required to stop a car of mass 800 kg, moving at a speed of \[20\text{ }m{{s}^{-1}}\] over a distance of 25m in 2.5 sec is
  A)
  1200N done clear
  B)
  6400 N done clear
  C)
  1600N done clear
  D)
  1800N done clear
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• question_answer23)
  A boy, sitting on the topmost birth in the compartment of a train which is just going to stop on the railway station, drops an apple aiming at the open hand of his brother situated vertically below his own hand at a distance of 2m. The apple will fall
  A)
  in the hand of his brother done clear
  B)
  slightly away from the hand of his brother in the direction of motion of the train done clear
  C)
  slightly away from the hand of his brother opposite to the direction of motion of the train done clear
  D)
  None of the above done clear
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• question_answer24)
  A shopper pushes a shopping cart of a store with a constant force of 75 N [forward]. The shopping cart exerts a force of 75 N [backward] on the shopper
  A)
  only if the velocity of the cart is constant. done clear
  B)
  only if there is no friction between the cart and the floor. done clear
  C)
  only if the velocity of the cart is increasing. done clear
  D)
  system to be the shopper and cart. done clear
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• question_answer25)
  A block is placed on a rough horizontal plane. A time dependent horizontal force \[\text{F = kt}\]acts on the block, where k is a positive constant. The acceleration - time graph of the block is:
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
    done clear
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• question_answer26)
  A particle moves in the X-Y plane under the influence of force such that its linear momentum is\[\vec{p}(t)=-A[\hat{i}\cos (kt)-\hat{j}\sin (kt)]\], where A and k are constants. The angle between the force and the momentum is
  A)
  \[0{}^\circ \] done clear
  B)
  \[30{}^\circ \]   done clear
  C)
  \[45{}^\circ \] done clear
  D)
  \[90{}^\circ \] done clear
  View Solution play_arrow

• question_answer27)
  A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by:
  A)
  68% done clear
  B)
  41% done clear
  C)
  200% done clear
  D)
  100% done clear
  View Solution play_arrow

• question_answer28)
  Sand is being dropped on a conveyor belt at the rate of\[\text{M kg/s}\]. The force (in N) necessary to keep the belt moving with a constant velocity of \[\text{v m/s}\] will be:
  A)
  \[\text{Mv}\] done clear
  B)
  \[\text{2 Mv}\] done clear
  C)
  \[\frac{\text{Mv}\,}{2}\] done clear
  D)
  \[\frac{\text{Mv}\,}{3}\] done clear
  View Solution play_arrow

• question_answer29)
  If a cricketer catches a ball of mass \[150\text{ }gm\]moving with a velocity of\[20\text{ }m/s\], then he experiences a force of (Time taken to complete the catch is sec.)
  A)
  300 N   done clear
  B)
  30 N done clear
  C)
  3 N   done clear
  D)
  0.3 N done clear
  View Solution play_arrow

• question_answer30)
  . A bullet is fired from a gun. The force on the bullet is given by \[F=600-2\times {{10}^{5}}t\]where. F is in newton and t in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?
  A)
  1.8 N-s  done clear
  B)
  zero  done clear
  C)
  9 N-s done clear
  D)
  0.9 N-s done clear
  View Solution play_arrow

• question_answer31)
  A 5000 kg rocket is set for vertical firing. The exhaust speed is\[800m{{s}^{-1}}\]. To give an initial upward acceleration of\[20m{{s}^{-2}}\], the amount of gas ejected per second to supply the needed thrust will be \[\left( g=10m{{s}^{-2}} \right)\]
  A)
  \[127.5\text{ }kg\text{ }{{s}^{-1}}\] done clear
  B)
  \[187.5\text{ }kg\text{ }{{s}^{-1}}\] done clear
  C)
  \[185.5\text{ }kg\text{ }{{s}^{-1}}\] done clear
  D)
  \[137.5\text{ }kg\text{ }{{s}^{-1}}\] done clear
  View Solution play_arrow

• question_answer32)
  A satellite in a force free space sweeps stationary interplanetary dust at a rate\[\left( dM/dt \right)\,=av\]. The acceleration of satellite is
  A)
  \[\frac{-2\alpha {{v}^{2}}}{M}\] done clear
  B)
  \[\frac{-\alpha {{v}^{2}}}{M}\] done clear
  C)
  \[\frac{-\alpha {{v}^{2}}}{2M}\] done clear
  D)
  \[-\alpha {{v}^{2}}\] done clear
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• question_answer33)
  A particle of mass m is made to move with uniform speed v along the perimeter of a regular polygon of n sides, inscribed in a circle of radius a. The magnitude of impulse applied at each comer of the polygon is :
  A)
  \[2mv\sin \frac{\pi }{n}\]   done clear
  B)
  \[mv\sin \frac{\pi }{n}\] done clear
  C)
  \[mv\sin \frac{n}{\pi }\]   done clear
  D)
  \[mv\sin \frac{n}{\pi }\] done clear
  View Solution play_arrow

• question_answer34)
  The force 'F' acting on a particle of mass 'm' is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is:
  A)
  24 Ns done clear
  B)
  20 Ns done clear
  C)
  12 Ns done clear
  D)
  6 Ns done clear
  View Solution play_arrow

• question_answer35)
  For the given situation as shown in the figure, the value of \[\theta \] to keep the system in equilibrium will be          
  A)
  \[30{}^\circ \] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[0{}^\circ \] done clear
  D)
  \[90{}^\circ \] done clear
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• question_answer36)
  If the coefficient of friction between all surfaces is 0.5, then find the minimum force F to have equilibrium of system. (assume strings and pulleys are massless)    
  A)
  \[\frac{4000}{17}N\] done clear
  B)
  \[\frac{1000}{17}N\,\] done clear
  C)
  \[\frac{2000}{17}N\,\] done clear
  D)
  \[\frac{500}{17}N\,\] done clear
  View Solution play_arrow

• question_answer37)
  A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration\[1.0\text{ }m/{{s}^{2}}\]. If \[g=\text{ }10\text{ }m{{s}^{-2}}\], the tension in the supporting cable is
  A)
  8600 N   done clear
  B)
  9680 N done clear
  C)
  11000 N   done clear
  D)
  1200 N done clear
  View Solution play_arrow

• question_answer38)
  If two masses (M & m) are connected on a horizontal plane and a force is applied on the combination, then the tension T depends on the
  A)
  force applied on the system done clear
  B)
  whether force is applied on M or m done clear
  C)
  both [a] and [b] done clear
  D)
  Can't be predicted. done clear
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• question_answer39)
  A solid sphere of 2 kg is suspended from a horizontal beam by two supporting wires as shown in fig. Tension in each wire is approximately \[\left( g=\text{ }10m{{s}^{-2}} \right)\]
  A)
  30 N   done clear
  B)
  20 N done clear
  C)
  10 N   done clear
  D)
  5 N done clear
  View Solution play_arrow

• question_answer40)
  Three identical blocks of masses \[m=2\text{ }kg\]are drawn by a force \[F=\text{ }10.2\text{ }N\] with an acceleration of \[0.6\text{ }m{{s}^{-2}}\] on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C?
  A)
  92 done clear
  B)
  3.4    done clear
  C)
  4  done clear
  D)
  9.8 done clear
  View Solution play_arrow

• question_answer41)
  A 1 kg block and a 0.5 kg block move together on a horizontal frictionless surface. Each block exerts a force of 6 N on the other. The block move with a uniform acceleration of
  A)
  \[\,3\text{ }m{{s}^{-2}}\] done clear
  B)
  \[\text{6 }m{{s}^{-2}}\] done clear
  C)
  \[9\text{ }m{{s}^{-2}}\] done clear
  D)
  \[\text{12 }m{{s}^{-2}}\] done clear
  View Solution play_arrow

• question_answer42)
  For the system shown in figure, the correct expression is
  A)
  \[{{F}_{3}}={{F}_{1}}+F{{  }_{2}}\]   done clear
  B)
  \[{{F}_{3}}=\frac{{{m}_{3}}F}{{{F}_{1}}+F{{  }_{2}}+{{F}_{3}}}\] done clear
  C)
  \[{{F}_{3}}=\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\]          done clear
  D)
  \[\,{{F}_{3}}=\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}}\] done clear
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• question_answer43)
  Which of the following is true about acceleration, for the system?         
  A)
  Acceleration is more in A, when force is applied on A. done clear
  B)
  Acceleration is more in B, when force is applied on B. done clear
  C)
  Acceleration is same and does not depend on whether the force is applied on \[\,{{m}_{1}}\] or \[\,{{m}_{2}}\] done clear
  D)
  Acceleration depends on the tension in the tiring. done clear
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• question_answer44)
  Two blocks of masses 2 kg and 4 kg are attached by an inextensible light string as shown in the figure. If a force of 120 N pulls the blocks vertically upward, the tension in the string is (Take\[g\text{ }=\text{ }10\text{ }m{{s}^{-2}}\])               
  A)
  20N done clear
  B)
  15N done clear
  C)
  35N done clear
  D)
  40N done clear
  View Solution play_arrow

• question_answer45)
  A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of \[5\text{ }m/{{s}^{2}}\], the reading of the spring balance will be
  A)
  24N done clear
  B)
  74N done clear
  C)
  15N done clear
  D)
  49N done clear
  View Solution play_arrow

• question_answer46)
  The elevator shown in fig. is descending with an acceleration of\[2\text{ }m/{{s}^{2}}\]. The mass of the block \[A=0.5\text{ }kg.\] The force exerted by the block A on block B is
  A)
  2N  done clear
  B)
  4N done clear
  C)
  6N done clear
  D)
  8N done clear
  View Solution play_arrow

• question_answer47)
  A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end. The acceleration of the system is (given \[g=10m{{s}^{-2}}\]) 
  A)
  \[100m/{{s}^{-2}}\]   done clear
  B)
  \[3m/{{s}^{-2}}\] done clear
  C)
  \[10m/{{s}^{-2}}\]   done clear
  D)
  \[30m/{{s}^{-2}}\] done clear
  View Solution play_arrow

• question_answer48)
  A triangular block of mass M with angles\[30{}^\circ \],\[~60{}^\circ \], and \[90{}^\circ \] rests with its \[30{}^\circ -90{}^\circ \]side on a horizontal table. A cubical block of mass m rests on the \[60{}^\circ -30{}^\circ \] side. The acceleration which M must have relative to the table to keep m stationary relative to the triangular block assuming frictionless contact is     
  A)
  \[g\] done clear
  B)
  \[\frac{g}{\sqrt{2}}\] done clear
  C)
  (c)\[\frac{g}{\sqrt{3}}\] done clear
  D)
  \[\frac{g}{\sqrt{5}}\] done clear
  View Solution play_arrow

• question_answer49)
  An overweight acrobat, "weighing" in at 115 kg, wants to perform a single hand stand. He tries to cheat by resting one foot against a smooth frictionless vertical wall. The horizontal force there is 130 N. What is the magnitude of the force exerted by the floor on his hand? Answer in N.
  A)
  1134     done clear
  B)
  1257 done clear
  C)
  997       done clear
  D)
  1119 done clear
  View Solution play_arrow

• question_answer50)
  A monkey of mass 20 kg is holding a vertical rope. The rope will not break when a mass of 25 g is suspended from it but will break if the mass exceeds 25 kg. What is the maximum acceleration with which the monkey can climb up along the rope? \[\left( g=10\text{ }m/{{s}^{2}} \right)\]
  A)
  \[2.5\text{ }m/s\]   done clear
  B)
  \[5\text{ }m/{{s}^{2}}\] done clear
  C)
  \[\text{10 }m/{{s}^{2}}\]     done clear
  D)
  \[\text{25 }m/{{s}^{2}}\] done clear
  View Solution play_arrow

• question_answer51)
  Two blocks \[{{m}_{1}}=5gm\] and\[{{m}_{2}}=\text{10}gm\] are hung vertically over a light frictionless pulley as shown here. What is the acceleration of the masses when they are left free? (Where g is acceleration due to gravity)
  A)
  \[g/3\]   done clear
  B)
  \[g/2\] done clear
  C)
  \[g\]        done clear
  D)
  \[g/5\] done clear
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• question_answer52)
  In the figure (i) an extensible string is fixed at one end and the other end is pulled by a tension T. In figure (ii) another identical string is pulled by tension T at both the ends. The ratio of elongation in equilibrium of string in (i) to the elongation of string in (ii) is
  A)
  \[1:1\] done clear
  B)
  \[1:2\] done clear
  C)
  \[2:1\] done clear
  D)
  (d)\[0\] done clear
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• question_answer53)
  Two monkeys of masses 10 kg and 8 kg are moving along a vertical rope which is light and inextensible, the former climbing up with an acceleration of \[2m/{{s}^{2}}\] while the latter coming down with a uniform velocity of \[2m/s\]. Find the tension (in newtons).
  A)
  200 N   done clear
  B)
  150 N done clear
  C)
  300 N   done clear
  D)
  100 N done clear
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• question_answer54)
  A weight W is supported by two cables as shown. The tension in the cable making angle \[\theta \] with horizontal will be the minimum when the value of \[\theta \] is.
  A)
  0           done clear
  B)
          \[30{}^\circ \]    done clear
  C)
  \[60{}^\circ \]                 done clear
  D)
  \[45{}^\circ \] done clear
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• question_answer55)
  For the arrangement shown in the figure let a and T be the acceleration of the blocks and tension in the string respectively. The string and the pulley are frictionless and massless. Which of the graphs show the correct relationship between 'a' and T in the system in which sum of the two masses \[{{m}_{1}}\] and \[{{m}_{2}}\]is constant?      
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer56)
  A body of mass 5 kg under the action of constant force \[\vec{F}={{F}_{x}}\hat{i}+{{F}_{y}}\hat{j}\] has velocity at \[t=0\text{ }s\] as \[\vec{v}=(6\hat{i}-2\hat{j})m/s\]and at \[t=\text{1}0\text{ }s\]gas\[\vec{v}=6\hat{j}\text{ m/s}\]. The force F is:
  A)
  \[\left( -3\hat{i}+4\hat{j} \right)\text{ N}\]            done clear
  B)
  \[\left( -\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j} \right)\text{ N}\] done clear
  C)
  \[\left( 3\hat{i}-4\hat{j} \right)\text{ N}\]   done clear
  D)
  \[\left( \frac{3}{5}\hat{i}-\frac{4}{5}\hat{j} \right)\text{ N}\] done clear
  View Solution play_arrow

• question_answer57)
  A pail filled with sand has a total mass of 60 kg. A crane is lowering it such that it has an initial downward acceleration of\[1.5\text{ }m/{{s}^{2}}\]. A hole in the pail allows sand to leak out. If the force exerted by the crane on the pail does not change, what mass of sand must leak out before the downward acceleration decreases to zero?
  A)
  9.2 kg     done clear
  B)
  20 kg done clear
  C)
  40 kg     done clear
  D)
  51 kg done clear
  View Solution play_arrow

• question_answer58)
  . One end of a massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in\[m{{s}^{-2}}\]) can a man of 60 kg climb on the rope?
  A)
  16 done clear
  B)
  6     done clear
  C)
  4 done clear
  D)
  8 done clear
  View Solution play_arrow

• question_answer59)
  A smooth ring P of mass m can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley and carries a block Q of mass (mil) as shown in the figure. At an instant, the string between the ring and the pulley makes an angle \[60{}^\circ \]with the rod. The initial acceleration of the ring is
  A)
  \[\frac{2g}{3}\]   done clear
  B)
  \[\frac{2g}{6}\] done clear
  C)
  \[\frac{2g}{9}\]   done clear
  D)
  \[\frac{g}{3}\] done clear
  View Solution play_arrow

• question_answer60)
  A horizontal uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by force F. What is the tension in the rope in a distance l from the end where the force is applied?
  A)
  (a)\[F\left( 1-\frac{l}{L} \right)\]   done clear
  B)
  \[2F\left( 1-\frac{l}{2L} \right)\] done clear
  C)
  \[\frac{F}{L}\]   done clear
  D)
  \[\frac{F}{l}\left( 1-\frac{l}{L} \right)\] done clear
  View Solution play_arrow

• question_answer61)
  In the figure acceleration of bodies A, B and C are shown with directions. Values b and c are w.r.t. ground whereas a is acceleration of block A w.r.t. sedge C. Acceleration of block A w.r.t. ground is
  A)
  \[\sqrt{{{\left( b+c \right)}^{2}}+{{a}^{2}}}\] done clear
  B)
         \[c-\left( a+b \right)\cos \theta \] done clear
  C)
  \[\sqrt{{{\left( b+c \right)}^{2}}+{{c}^{2}}-2\left( b+c \right).c.\cos \theta }\]     done clear
  D)
  \[\sqrt{{{\left( b+c \right)}^{2}}+{{c}^{2}}+2\left( b+c \right).c.\cos \theta }\] done clear
  View Solution play_arrow

• question_answer62)
  Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area a passing over a frictionless fixed pulley as shown in the figure. The system is then released. If \[M=2\], then the tension per unit crossectional area produced in the wire is
  A)
  \[\frac{2mg}{3A}\]   done clear
  B)
  \[\frac{4mg}{3A}\] done clear
  C)
  \[\frac{mg}{A}\]     done clear
  D)
  \[\frac{3mg}{4A}\] done clear
  View Solution play_arrow

• question_answer63)
  A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes up to 2 m height further, find the magnitude of the force. (Consider\[\,g\text{ }=\text{ }10\text{ }m/{{s}^{2}}\]).
  A)
  4 N       done clear
  B)
  16 N done clear
  C)
  20 N     done clear
  D)
  22 N done clear
  View Solution play_arrow

• question_answer64)
              A uniform sphere of weight W and radius 5 cm is being held by a string as shown in the figure. The tension in the string will be:
  A)
  \[12\frac{W}{5}\]  done clear
  B)
  \[5\frac{W}{12}\] done clear
  C)
  \[13\frac{W}{5}\] done clear
  D)
  \[13\frac{W}{12}\] done clear
  View Solution play_arrow

• question_answer65)
  Two blocks of mass \[{{M}_{1}}=\text{ }20\text{ }kg\]and \[{{M}_{2}}=\text{ }12\text{ }kg\]are connected by a metal rod of mass 8 kg. The system is pulled vertically up by applying a force of 480 N as shown. The tension at the mid-point of the rod is:
  A)
  144 N done clear
  B)
  96 N done clear
  C)
  240 N done clear
  D)
  192 N done clear
  View Solution play_arrow

• question_answer66)
  Two smooth cylindrical bars weighing W each lie next to each other in contact. A similar third bar is placed over the two bars as shown in figure. Neglecting friction, the minimum horizontal force on each lower bar necessary to keep them together is
  A)
  \[\frac{W}{2}\]   done clear
  B)
  \[W\] done clear
  C)
  \[\frac{W}{\sqrt{3}}\]   done clear
  D)
  \[\frac{W}{2\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer67)
              A string of negligible mass going over a clamped pulley of mass m supports a block of mass Mas shown in the figure. The force on the pulley by the clamp is given by      
  A)
  \[\sqrt{2}\text{ Mg}\] done clear
  B)
  \[\sqrt{2}\text{ mg}\] done clear
  C)
  \[\sqrt{{{\left( M+m \right)}^{2}}+{{m}^{2}}}\text{ g}\] done clear
  D)
  \[\sqrt{{{\left( M+m \right)}^{2}}+{{M}^{2}}}\text{ g}\] done clear
  View Solution play_arrow

• question_answer68)
  The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is\[\mu \]. The inclination \[\theta \] of the plane is
  A)
  \[{{\tan }^{-1}}\mu \] done clear
  B)
  \[{{\tan }^{-1}}\left( \mu /2 \right)\] done clear
  C)
  \[{{\tan }^{-1}}2\mu \] done clear
  D)
  \[{{\tan }^{-1}}3\mu \] done clear
  View Solution play_arrow

• question_answer69)
  A system shown in the figure. Assume that cylinder remains in contact with the sedge and block hence the velocity of cylinder is
  A)
  \[\frac{\sqrt{19-4\sqrt{3}}}{2}\text{ m/s}\] done clear
  B)
  \[\frac{\sqrt{13}}{2}\text{ m/s}\] done clear
  C)
  \[\sqrt{3}\text{m/s}\] done clear
  D)
  \[\sqrt{7}\text{ m/s}\] done clear
  View Solution play_arrow

• question_answer70)
  A conveyor belt is moving at a constant speed of 2m/s. A box is gently dropped on it. The coefficient of friction between them is\[\mu =0.5\]. The distance that the box will move relative to belt before coming to rest on it taking \[g=10m{{s}^{-2}}\], is
  A)
  1.2 m done clear
  B)
  0.6 m done clear
  C)
  zero done clear
  D)
  0.4 m done clear
  View Solution play_arrow

• question_answer71)
  A uniform rod AB of length 3r remains in equilibrium on a hemispherical bowl of radius r as shown in figure. Ignoring friction, the inclination of the rod \[\theta \]with the horizontal is
  A)
  \[{{\cos }^{-1}}\left( 1/3 \right)\] done clear
  B)
  \[{{\sin }^{-1}}\left( 1/3 \right)\] done clear
  C)
  \[{{\cos }^{-1}}\left( 0.9 \right)\] done clear
  D)
  \[{{\sin }^{-1}}\left( 0.9 \right)\] done clear
  View Solution play_arrow

• question_answer72)
  The upper half of an inclined plane of inclination \[\theta \]is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by
  A)
  \[\mu =\frac{2}{\tan \theta }\] done clear
  B)
  \[\mu =2\tan \theta \] done clear
  C)
  \[\mu =2\tan \theta \] done clear
  D)
  \[\mu =\frac{1}{\tan \theta }\] done clear
  View Solution play_arrow

• question_answer73)
  A 20 kg block B is suspended from a cord attached to a 40 kg cart A. Find the ratio of the acceleration of block in cases (i) and (ii) shown in the figure immediately after the system is released from rest. (neglect friction)
  A)
  \[\frac{\sqrt{2}}{3}\]   done clear
  B)
  \[3\sqrt{2}\] done clear
  C)
   \[\frac{3}{2}\]   done clear
  D)
  \[\frac{3}{2\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer74)
  In the diagram shown, friction is completely absent. If a force F has been applied on the wedge such that it moves with a constant velocity than value of normal reaction N' is
  A)
  \[>F\] done clear
  B)
  \[<F\] done clear
  C)
  \[=F\] done clear
  D)
  cannot find done clear
  View Solution play_arrow

• question_answer75)
  It is difficult to move a cycle with brakes on because
  A)
  rolling friction opposes motion on road done clear
  B)
  sliding friction opposes motion on road done clear
  C)
  rolling friction is more than sliding friction done clear
  D)
  sliding friction is more than rolling friction done clear
  View Solution play_arrow

• question_answer76)
  The acceleration of the system shown in the figure is given by the expression (coefficient of friction between m, and surface is \[\mu \])            
  A)
  \[a=\frac{\left( {{m}_{2}}-\mu {{m}_{1}} \right)}{\left( {{m}_{1}}+{{m}_{2}} \right)}\] done clear
  B)
  \[a=\frac{{{m}_{1}}g}{\left( {{m}_{1}}+{{m}_{2}} \right)}\] done clear
  C)
  \[a=\frac{\left( {{m}_{1}}+\mu {{m}_{2}} \right)}{\left( {{m}_{1}}+{{m}_{2}} \right)g}\] done clear
  D)
         \[a=\frac{\left( {{m}_{1}}-{{m}_{2}} \right)\mu }{\left( {{m}_{1}}+{{m}_{2}} \right)g}\] done clear
  View Solution play_arrow

• question_answer77)
  A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is
  A)
  20 N   done clear
  B)
  50 N done clear
  C)
  100 N   done clear
  D)
  2 N done clear
  View Solution play_arrow

• question_answer78)
  A block B is pushed momentarily along a horizontal surface with an initial velocity V. If p is the coefficient of sliding friction between Band the surface, block B will come to rest after a time
  A)
  \[\frac{g\mu }{V}\]   done clear
  B)
  \[\frac{g}{V}\] done clear
  C)
  \[\frac{V}{g}\]   done clear
  D)
  \[\frac{V}{g\left( \mu  \right)}\] done clear
  View Solution play_arrow

• question_answer79)
  A small mass slides down a fixed inclined plane of inclination 6 with the horizontal. The coefficient of friction is \[\mu \text{ }=\text{ }{{\mu }_{0}}x\]Where \[x\] is the distance through which the mass slides down and \[{{\mu }_{0}}\] is a constant? Then he speed is maximum after the mass covers a distance of
  A)
  \[\frac{\cos \theta }{{{\mu }_{0}}}\] done clear
  B)
  \[\frac{\sin \theta }{{{\mu }_{0}}}\] done clear
  C)
  \[\frac{tan\theta }{{{\mu }_{0}}}\] done clear
  D)
  \[\frac{2tan\theta }{{{\mu }_{0}}}\] done clear
  View Solution play_arrow

• question_answer80)
  Two identical smooth surfaced solid cylinders of radius r are placed touching along their lengths on a horizontal surface. A third cylinder of same material but twice the radius of that of the cylinders is placed lengthwise on them so that the system remains at rest. If all three cylinders have the same length, then minimum value of the coefficient of friction between smaller cylinders and the surface is:          
  A)
  \[\frac{1}{\sqrt{2}}\]   done clear
  B)
  \[\frac{1}{3}\] done clear
  C)
  \[\frac{1}{3\sqrt{2}}\]   done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer81)
  A block is placed on a rough inclined plane. The angle of the incline,\[\theta \] is slowly increased from the horizontal position. At a certain angle, the block starts to slide along the plane. The angle of the incline is increased further. Consider the following graphs: (I)           (II) (III)       (IV) Which of the above graphs correctly depicts the variation of the fractional force, f, exerted by the plane on the block, as a function of\[\theta \]? (Assume that the block does not topple.)
  A)
  I         done clear
  B)
  II done clear
  C)
  III done clear
  D)
  IV done clear
  View Solution play_arrow

• question_answer82)
  The minimum force required to start pushing a body up rough (frictional coefficient u) inclined plane is \[{{F}_{1}}\]while the minimum force needed to prevent it from sliding down is\[{{F}_{2}}\]. If the inclined plane makes an angle \[\theta \] from the horizontal such that\[\tan \theta =2\mu \] then the ratio \[\frac{{{F}_{1}}}{{{F}_{2}}}\] is
  A)
  1          done clear
  B)
  2      done clear
  C)
  3          done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer83)
  A body starts from rest on a long inclined plane of slope\[45{}^\circ \]. The coefficient of friction between the body and the plane varies as\[u=0.3\text{ }x\], where \[x\]is distance travelled down the plane. The body will have maximum speed (For\[g=10\text{ }m/{{s}^{2}}\]) when \[x=\]
  A)
  9.8 m     done clear
  B)
  27 m done clear
  C)
  12 m     done clear
  D)
  3.33 m done clear
  View Solution play_arrow

• question_answer84)
  A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied to B for the blocks to move together will be:
  A)
  30 N done clear
  B)
  25 N done clear
  C)
  27 N done clear
  D)
  48 N done clear
  View Solution play_arrow

• question_answer85)
  The two blocks, \[m=10\text{ }kg\]and \[M=50\text{ }kg\]are free to move as shown. The coefficient of static friction between the blocks is 0.5 and there is no friction between M and the ground. A minimum horizontal force F is applied to hold m against M that is equal to
  A)
  100 N done clear
  B)
  50 N done clear
  C)
  240 N done clear
  D)
  180 N done clear
  View Solution play_arrow

• question_answer86)
  A given object takes n times as much time to slide down a \[45{}^\circ \] rough incline as it takes to slide down a perfectly smooth\[45{}^\circ \]incline. The coefficient of friction between the object and the incline is
  A)
  \[\left( 1-1/{{n}^{2}} \right)\] done clear
  B)
  \[1/\left( 1-{{n}^{2}} \right)\] done clear
  C)
  \[\sqrt{\left( 1-1/{{n}^{2}} \right)}\] done clear
  D)
  \[1/\sqrt{\left( 1-{{n}^{2}} \right)}\] done clear
  View Solution play_arrow

• question_answer87)
  A block of mass m = 2 kg is placed on a plank of mass \[M=10\text{ }kg\]which is placed on a smooth horizontal plane. The coefficient of friction between the block and the plank is\[\mu =\frac{1}{3}\]. If a horizontal force F is applied on the plank, then find the maximum value of F for which the block and the plank move together. (Take \[g=10\text{ }m/{{s}^{2}}\])
  A)
  30 N   done clear
  B)
  40 N done clear
  C)
  120 N              done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer88)
  If u be the coefficient of friction between the block and the cart, horizontal acceleration of the cart that is required to prevent block B from faffing is:              
  A)
  \[\mu /g\] done clear
  B)
  \[g/\mu \] done clear
  C)
  \[g\] done clear
  D)
  \[\left( {{\mu }^{2}}+1 \right)g\] done clear
  View Solution play_arrow

• question_answer89)
  An insect of mass m, starts moving on a rough inclined surface from point A. As the surface is very sticky, the coefficient of friction between the insect and the incline is\[\mu \text{ }=\text{ }1\]. Assume that it can move in any direction, up the incline or down the incline then
  A)
  The maximum possible acceleration of the insect can be \[14\text{ }m/{{s}^{2}}\] done clear
  B)
  The maximum possible acceleration of the insect can be \[\text{2 }m/{{s}^{2}}\] done clear
  C)
  the insect can move with a constant velocity   done clear
  D)
  the insect cannot move with a constant velocity done clear
  View Solution play_arrow

• question_answer90)
  A particle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down is
  A)
  \[\sqrt{gR}\] done clear
  B)
  \[\sqrt{2gR}\] done clear
  C)
  \[\sqrt{3gR}\] done clear
  D)
  \[\sqrt{5gR}\] done clear
  View Solution play_arrow

• question_answer91)
  A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A bob is suspended from the roof of the car by a light wire of length 1.0 m. The angle made by the wire with the vertical is
  A)
  \[0{}^\circ \]   done clear
  B)
  \[\frac{\pi }{3}\] done clear
  C)
  \[\frac{\pi }{6}\]   done clear
  D)
  \[\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer92)
  A particle of mass m rotates with a uniform angular speed\[\omega \]. It is viewed from a frame rotating about the z-axis with a uniform angular velocity\[{{\omega }_{0}}\]. The centrifugal force on the particle is:
  A)
  \[m{{\omega }^{2}}r\] done clear
  B)
  \[m{{\omega }^{2}}r\] done clear
  C)
  \[m\left( \frac{\omega +{{\omega }_{0}}}{2} \right)a\] done clear
  D)
  zero done clear
  View Solution play_arrow

• question_answer93)
  A bridge is in the form of a semi-circle of radius 40m. The greatest speed with which a motor cycle can cross the bridge without leaving the ground at the highest point is \[\left( g=10\text{ }m{{s}^{-2}} \right)\] (frictional force is negligibly small)
  A)
  \[40\text{ }m{{s}^{-1}}\] done clear
  B)
  \[20\text{ }m{{s}^{-1}}\] done clear
  C)
  \[30\text{ }m{{s}^{-1}}\] done clear
  D)
  \[\text{15 }m{{s}^{-1}}\] done clear
  View Solution play_arrow

• question_answer94)
  A particle tied to a string describes a vertical circular motion of radius r continually. If it has a velocity \[\sqrt{3gr}\] at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is
  A)
  \[4:3\] done clear
  B)
  \[5:4\]   done clear
  C)
  \[1:4\] done clear
  D)
  \[3:2\] done clear
  View Solution play_arrow

• question_answer95)
  An aircraft executes a horizontal loop with a speed of 150 m/s with its wings banked at an angle of \[12{}^\circ .\] The radius of the loop is : \[\left( g=10m/{{s}^{2}} \right)\]
  A)
  10.6 km done clear
  B)
  9.6 km done clear
  C)
  7.4 km done clear
  D)
  5.8 km done clear
  View Solution play_arrow

• question_answer96)
  In the given figure, a smooth parabolic wire track lies in the xy-plane (vertical). The shape of track is defined by the equation\[y={{x}^{2}}\]. A ring of mass m which can slide freely on the wire track, is placed at the position A (1,1). The track is rotated with constant angular speed to such there is no relative slipping between the ring and the track. The value of \[\omega \] is        
  A)
  \[\sqrt{g/2}\] done clear
  B)
  \[\sqrt{g}\] done clear
  C)
  \[\sqrt{2g}\] done clear
  D)
  \[2\sqrt{g}\] done clear
  View Solution play_arrow

• question_answer97)
  A conical pendulum of length 1 m makes an angle \[\theta =45{}^\circ \] w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below 0. The speed of the pendulum, in its circular path, will be:   (Take \[g=10m{{s}^{-2}}\])
  A)
  0.4 m/s done clear
  B)
  4 m/s done clear
  C)
  0.2 m/s done clear
  D)
  2 m/s done clear
  View Solution play_arrow

• question_answer98)
  A car is negotiating a curved road of radius R. The road is banked at an angle\[\theta \]. The coefficient of friction between the tyres of the car and the road is\[{{\mu }_{s}}\]. The maximum safe velocity on this road is:
  A)
  \[\sqrt{g{{R}^{2}}\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\] done clear
  B)
  \[\sqrt{gR\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\] done clear
  C)
  \[\sqrt{\frac{g}{R}\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\] done clear
  D)
  \[\sqrt{\frac{g}{{{R}^{2}}}\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\] done clear
  View Solution play_arrow

• question_answer99)
  A particle is moving along a circular path in the xy plane (see figure). When it crosses the x-axis, it has an acceleration along the path of\[1.5\text{ }m/{{s}^{2}}\], and is moving with a speed of 10 m/s in the negatives-direction. The total acceleration of the particle is:      
  A)
  \[50\hat{i}-1.5\hat{j}\text{ m/}{{\text{s}}^{2}}\] done clear
  B)
  \[-50\hat{i}-1.5\hat{j}\text{ m/}{{\text{s}}^{2}}\] done clear
  C)
  \[10\hat{i}-1.5\hat{j}\text{ m/}{{\text{s}}^{2}}\] done clear
  D)
  \[1.5\hat{i}-50\hat{j}\text{ m/}{{\text{s}}^{2}}\] done clear
  View Solution play_arrow

• question_answer100)
  Two particles of equal mass are connected to a rope AB of negligible mass such that one is at end A and other dividing the length of rope in the ratio \[1:2\]from B. The rope is rotated about end B in a horizontal plane. Ratio of tensions in the smaller part to the other is (ignore effect of gravity)                   
  A)
  \[4:3~\] done clear
  B)
  \[1:4\] done clear
  C)
  \[1:2\] done clear
  D)
  \[1:3\] done clear
  View Solution play_arrow