# Solved papers for NEET Physics NLM, Friction, Circular Motion NEET PYQ-NLM Friction Circular Motion

### done NEET PYQ-NLM Friction Circular Motion Total Questions - 71

• question_answer1)  Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the right is $10\text{ }m/s$. What is the velocity of B when angle$\alpha ={{60}^{o}}$? [AIPMT 1998] A)
9.8 m/s

B)
10 m/s

C)
5.8 m/s

D)
17.3 m/s

• question_answer2)  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 m/s. The ratio of the tensions is:         [AIPMT 1998]

A)
3 : 1

B)
1 : 3

C)
1 : 2

D)
2 : 1

• question_answer3) 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?                             [AIPMT 1998]

A)
8 Ns

B)
Zero

C)
0.9 Ns

D)
1.8 Ns

• question_answer4) A 5000 kg rocket is set for vertical firing. The exhaust speed is $800\text{ }m{{s}^{-1}}$. To give an initial upward acceleration  of $20\text{ }m/{{s}^{2}},$ the amount of gas ejected per second to supply the needed thrust will be : $(g=10\text{ }m{{s}^{-2}})$ [AIPMT 1998]

A)
$127.5\text{ }kg\text{ }{{s}^{-1}}$

B)
$187.5\text{ }kg\text{ }{{s}^{-1}}$

C)
$185.5\text{ }kg\text{ }{{s}^{-1}}$

D)
$137.5\text{ }kg\text{ }{{s}^{-1}}$

• question_answer5) A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?    [AIPMT 1998]

A)
14 m/s

B)
3 m/s

C)
3.92 m/s

D)
5 m/s

• question_answer6)  O is the centre of an equilateral triangle ABC. ${{F}_{1}},\text{ }{{F}_{2}}$ and ${{F}_{3}}$ are three forces acting along the sides AB, BC and AC as shown in figure. What should be the magnitude of ${{F}_{3}}$ so that the total torque about O is zero? [AIPMT 1998]

A)
$({{F}_{1}}+{{F}_{2}})/2$

B)
$({{F}_{1}}-{{F}_{2}})$

C)
$({{F}_{1}}+{{F}_{2}})$

D)
$2\,({{F}_{1}}+{{F}_{2}})$

• question_answer7) A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/h. The centripetal force is: [AIPMT 1999]

A)
250 N

B)
750 N

C)
1000 N

D)
1200 N

• question_answer8) Two racing cars of masses ${{m}_{1}}$ and ${{m}_{2}}$ are moving in circles of radii ${{r}_{1}}$ and ${{r}_{2}}$ respectively. Their speeds are such that each makes a complete circle in the same time t. The ratio of the angular speeds of the first to the second car is: [AIPMT 1999]

A)
1 : 1

B)
${{m}_{1}}:\text{ }{{m}_{2}}$

C)
${{r}_{1}}:\text{ }{{r}_{2}}$

D)
${{m}_{1}}:\text{ }{{m}_{2}}:\text{ }{{r}_{1}}{{r}_{2}}$

• question_answer9) What is the linear velocity if angular velocity vector $\vec{\omega }=3\hat{i}-4\hat{j}+\hat{k}$ and position vector$\vec{r}=5\hat{i}-6\hat{j}+6\hat{k}\,$?             [AIPMT 1999]

A)
$6\hat{i}+2\hat{j}-3\hat{k}$

B)
$-18\hat{i}-13\hat{j}+2\hat{k}$

C)
$18\hat{i}+13\hat{j}-2\hat{k}$

D)
$6\hat{i}-2\hat{j}+8\hat{k}$

• question_answer10) The force on a rocket moving with a velocity $300\text{ }m/s$ is 210 N. The rate of consumption of fuel of rocket is:[AIPMT 1999]

A)
0.7 kg/s

B)
1.4 kg/s

C)
0.07 kg/s

D)
10.7 kg/s

• question_answer11)  A ball of mass 3 kg moving with a speed of 100 m/s, strikes a wall at an angle ${{60}^{o}}$ (as shown in figure). The ball rebounds at the same speed and remains in contact with the ball for 0.2 s, the force exerted by the ball on the wall is    [AIPMT 2000] A)
$1500\sqrt{3}\,N$

B)
1500 N

C)
$300\,\sqrt{3}\,N$

D)
300 N

• question_answer12)  Two masses ${{M}_{1}}=5\text{ }kg,\text{ }{{M}_{2}}=10\text{ }kg$ are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When masses are released, then acceleration of masses will be: [AIPMT 2000] A)
g

B)
$\frac{g}{2}$

C)
$\frac{g}{3}$

D)
$\frac{g}{4}$

• question_answer13) 1 kg body explodes into three fragments. The ratio of their masses is 1 : 1: 3. The fragments of same mass move perpendicular to each other with speeds 30 m/s, while the heavier part remains in the initial direction. The speed of heavier part is:                               [AIPMT 2001]

A)
$\frac{10}{\sqrt{2}}\,m/s$

B)
$10\sqrt{2}\,m/s$

C)
$20\sqrt{2}\,m/s$

D)
$30\sqrt{2}\,m/s$

• question_answer14) A particle of mass M is revolving along a circle of radius R and another particle of mass m is revolving in a circle of radius r. If time periods of both particles are same, then the ratio of their angular velocities is:              [AIPMT 2001]

A)
1

B)
$\frac{R}{r}$

C)
$\frac{r}{R}$

D)
$\sqrt{\frac{R}{r}}$

• question_answer15) In SHM restoring force is $F=-\text{ }kx,$ where k is force constant, x is displacement and A is amplitude of motion, then total energy depends upon:                                         [AIPMT 2001]

A)
k, A and M

B)
k, x, M

C)
k, A

D)
k, x

• question_answer16) A player takes 0.1 s in catching a ball of mass 150 g moving with velocity of 20 m/s. The force imparted by the ball on the hands of the player is:                                      [AIPMT 2001]

A)
0.3 N

B)
3 N

C)
30 N

D)
300 N

• question_answer17) A body attains a height equal to the radius of the earth. The velocity of the body with which it was projected is:                         [AIPMT 2001]

A)
$\sqrt{\frac{GM}{R}}$

B)
$\sqrt{\frac{2GM}{R}}$

C)
$\sqrt{\frac{5}{4}\,\frac{GM}{R}}$

D)
$\sqrt{\frac{3GM}{R}}$

• question_answer18) A block of mass 10 kg is placed on a rough horizontal surface having coefficient of friction $\mu =0.5$. If a horizontal force of 100 N is applied on it, then the acceleration of the block wilt be:$(g=10m/{{s}^{2}})$ [AIPMT 2002]

A)
$15\text{ }m/{{s}^{2}}$

B)
$10\text{ }m/{{s}^{2}}$

C)
$5\text{ }m/{{s}^{2}}$

D)
$0.5\text{ }m/{{s}^{2}}$

• question_answer19) A lift of mass 1000 kg is moving upwards with an acceleration of $1\text{ }m/{{s}^{2}}$. The tension developed in the string, which is connected to lift is: $(g=9.8\text{ }m/{{s}^{2}})$                                 [AIPMT 2002]

A)
9800 N

B)
10800 N

C)
11000 N

D)
10000 N

• question_answer20) A man weighs 80 kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of $5\text{ }m/{{s}^{2}}$. What would be the reading on the scale? $(g=10\text{ }m/{{s}^{2}})$ [AIPMT 2003]

A)
800 N

B)
1200 N

C)
Zero

D)
400 N

• question_answer21) A monkey of mass 20 kg is holding a vertical rope. The rope will not break when a mass of 25 kg 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? $(g=10\text{ }m/{{s}^{2}})$              [AIPMT 2003]

A)
$25\text{ }m/{{s}^{2}}$

B)
$2.5\text{ }m/{{s}^{2}}$

C)
$5\text{ }m/{{s}^{2}}$

D)
$10\text{ }m/{{s}^{2}}$

• question_answer22) A particle moves along a circle of radius $\left( \frac{20}{\pi } \right)\,m$ with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is: [AIPMT 2003]

A)
$160\,\,\pi \,m/{{s}^{2}}$

B)
$40\,m/{{s}^{2}}$

C)
$40\,\,\pi \,m/{{s}^{2}}$

D)
$640\,\,\pi \,m/{{s}^{2}}$

• question_answer23) A stationary particle explodes into two particles of masses ${{m}_{1}}$ and ${{m}_{2}}$ which move in opposite directions with velocities ${{v}_{1}}$ and ${{v}_{2}}$. The ratio of their kinetic energies ${{E}_{1}}/{{E}_{2}}$ is:   [AIPMT 2003]

A)
1

B)
${{m}_{1}}{{v}_{2}}/{{m}_{2}}{{v}_{1}}$

C)
${{m}_{2}}/{{m}_{1}}$

D)
${{m}_{1}}/{{m}_{2}}$

• question_answer24)  The coefficient of static friction, ${{\mu }_{s}}$ between block A of mass 2 kg and the table as shown in the figure, is 0.2. What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assumed to be smooth and mass less:$(g=10\text{ }m/{{s}^{2}})$ [AIPMT (S) 2004] A)
2.0 kg

B)
4.0 kg

C)
0.2 kg

D)
0.4 kg

• question_answer25) A block of mass m is placed on a smooth wedge of inclination $\theta$. 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:                                    [AIPMT (S) 2004]

A)
$mg\,\cos \theta$

B)
$mg\sin \theta$

C)
$mg$

D)
$mg/\cos \theta$

• question_answer26) A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 ms-1. The kinetic energy of the other mass is:                   [AIPMT (S) 2005]

A)
256 J

B)
486 J

C)
524 J

D)
324 J

• question_answer27) A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone?    [AIPMT (S) 2005]

A)
$\frac{\pi }{2}\,m{{s}^{-2}}$ and direction along the radius towards the centre

B)
${{\pi }^{2}}\,m{{s}^{-2}}$ and direction along the radius away from centre

C)
${{\pi }^{2}}\,m{{s}^{-2}}$ and direction along the radius towards the centre

D)
${{\pi }^{2}}\,m{{s}^{-2}}$ and direction along the tangent to the circle

• question_answer28)  A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of ${{30}^{o}}$ with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is:   [AIPMT (S) 2005] A)
48 N

B)
24 N

C)
12 N

D)
96 N

• question_answer29) A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity co. The force exerted by the liquid at the other end is: [AIPMT (S) 2005]

A)
$\frac{ML{{\omega }^{2}}}{2}$

B)
$\frac{M{{L}^{2}}\omega }{2}$

C)
$ML{{\omega }^{2}}$

D)
$\frac{M{{L}^{2}}{{\omega }^{2}}}{2}$

• question_answer30) A wheel has angular acceleration of $3.0\text{ }rad/{{s}^{2}}$ and an initial angular speed of$2.00\text{ }rad/s$. In a time of 2 s it has rotated through an angle (in radian) of:          [AIPMT (S) 2007]

A)
6

B)
10

C)
12

D)
4

• question_answer31)  A block B is pushed momentarily along a horizontal surface with an initial velocity v. If $\mu$ is the coefficient of sliding friction between B and the surface, blocks will come to rest after a time: [AIPMT (S) 2007] A)
$\frac{v}{g\mu }$

B)
$\frac{g\mu }{v}$

C)
$\frac{g}{v}$

D)
$\frac{v}{g}$

• question_answer32)  A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan?            [AIPMT (S) 2007] (Take $g=10m/{{s}^{2}}$) A)
8.0 cm

B)
10.0 cm

C)
Any value less than 12.0 cm

D)
4.0 cm

• question_answer33)  A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RQ are ${{F}_{1}},{{F}_{2}}$ and ${{F}_{3}}$ respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is                     [AIPMPT (S) 2008] A)
${{F}_{3}}-{{F}_{1}}-{{F}_{2}}$

B)
$\sqrt{{{({{F}_{3}}-{{F}_{1}})}^{2}}+F_{2}^{2}}$

C)
$\sqrt{{{({{F}_{3}}-{{F}_{1}})}^{2}}-F_{2}^{2}}$

D)
${{F}_{3}}-{{F}_{1}}+{{F}_{2}}$

• question_answer34) S and is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be                              [AIPMPT (S) 2008]

A)
Mv newton

B)
2 Mv newton

C)
$\frac{Mv}{2}$ newton

D)
zero

• question_answer35)  Three   forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is  [AIPMPT (S) 2008] A)
0.5 N

B)
1.5 N

C)
$\frac{\sqrt{3}}{4}N$

D)
$\sqrt{3}\,N$

• question_answer36)  A disc is rotating with angular velocity $(\omega )$ about its axis (without any translation push) on a smooth surface:[AIPMT (M) 2009] A)
Find direction and magnitude of velocity at points B and A.

B)
Why is friction necessary for rolling?

C)
What is direction of friction at point B?

D)
None of these

• question_answer37) An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of $12\,m{{s}^{-1}}$ and 2 kg second part moving with a velocity of $8\,m{{s}^{-1}}$. If the third part flies off with a velocity of  $4\,m{{s}^{-1}}$, its mass would be [AIPMT (S) 2009]

A)
5 kg

B)
7 kg

C)
17 kg

D)
3 kg

• question_answer38) The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is                           [AIPMT (S) 2009]

A)
$a=0,b=-1,c=-2$ downwards

B)
$_{Z}^{A}Z\xrightarrow[{}]{{}}{{\,}_{Z+}}_{1}^{4}Y\xrightarrow[{}]{{}}\,_{Z-1}^{A-4}{{B}^{*}}\xrightarrow[{}]{{}}\,_{Z-1}^{A-4}B,$ upwards

C)
$\beta ,\alpha ,\gamma$ downwards

D)
$\gamma ,\beta ,\alpha$ upwards

• question_answer39) A body, under the action of a force $\overrightarrow{E}=\hat{i}2xy+\hat{j}({{x}^{2}}+{{y}^{2}})+\hat{k}(3xz-{{y}^{2}})$ acquires an acceleration of $\overrightarrow{E}=\hat{i}{{z}^{3}}+\hat{j}xyz+\hat{k}{{z}^{2}}$. The mass of this body must be [AIPMT (S) 2009]

A)
$\overrightarrow{E}=\hat{i}(2xy-{{z}^{3}})+\hat{j}x{{y}^{2}}+\hat{k}3{{z}^{2}}x$

B)
10kg

C)
20kg

D)
$2\times {{10}^{4}}J{{T}^{-1}}$

• question_answer40)  A block of mass m is in contact with the cart C as shown in the figure. The coefficient of static friction between the block and the cart is y. The acceleration a of the cart that will prevent the block from falling satisfies [AIPMT (S) 2010]

A)
$\alpha >\frac{mg}{\mu }$

B)
$\alpha >\frac{g}{\mu m}$

C)
$\alpha \ge \frac{g}{\mu }$

D)
$\alpha <\frac{g}{\mu }$

• question_answer41) A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if              [AIPMT (S) 2010]

A)
$r=\mu g{{\omega }^{2}}$

B)
$r<\frac{{{\omega }^{2}}}{\mu g}$

C)
$r\le \frac{\mu g}{{{\omega }^{2}}}$

D)
$r\ge \frac{\mu g}{{{\omega }^{2}}}$

• question_answer42) A conveyor belt is moving at a constant speed of 2 m/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 $g=10\,\,m{{s}^{-2}},$ is [AIPMT (M) 2011]

A)
1.2 m

B)
0.6 m

C)
zero

D)
0.4 m

• question_answer43)  A small mass attached to a string rotates on frictionless table top as shown. If the tension is the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will [AIPMT (M) 2011] A)
remain constant

B)
increase by a factor of 2

C)
increase by a factor of 4

D)
decrease by a factor of 2

• question_answer44) A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 us. The acceleration of the particle is [AIPMT (S) 2011]

A)
$25\text{ }m/{{s}^{2}}$

B)
$36\text{ }m/{{s}^{2}}$

C)
$5\text{ }m/{{s}^{2}}$

D)
$15\text{ }m/{{s}^{2}}$

• question_answer45) 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 $g=10\text{ }m/{{s}^{2}},$ the tension in the supporting cable is [AIPMT (S) 2011]

A)
9680 N

B)
11000 N

C)
1200 N

D)
8600 N

• question_answer46) A car of mass m is moving on a level circular track of radius R. If ${{\mu }_{s}},$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by   [AIPMT (M) 2012]

A)
$\sqrt{{{\mu }_{s}}mRg}$

B)
$\sqrt{Rg/{{\mu }_{s}}}$

C)
$\sqrt{m\,Rg/{{\mu }_{s}}}$

D)
$\sqrt{{{\mu }_{s}}Rg}$

• question_answer47) A circular platform is mounted on a frictionless vertical axle. Its radius $R=2\,m$ and its moment of inertia about the axle is $200\text{ }kg\text{ }{{m}^{2}}$. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of $1\,\,m{{s}^{-1}}$ relative to the ground. Time taken by the man to complete one revolution is                       [AIPMT (M) 2012]

A)
$\pi \sec$

B)
$\frac{3\pi }{2}\sec$

C)
$2\pi \sec$

D)
$\frac{\pi }{2}\sec$

• question_answer48) A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is ${{45}^{o}},$ the speed of the car is [AIPMT (S) 2012]

A)
$20\,m{{s}^{-1}}$

B)
$30\,m{{s}^{-1}}$

C)
$5\,m{{s}^{-1}}$

D)
$10\,m{{s}^{-1}}$

• question_answer49)  Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity) [NEET 2013] A)
Zero

B)
2 mg

C)
3 mg

D)
6 mg

• question_answer50) The upper half of an inclined plane of inclination 9 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                                 [NEET 2013]

A)
$\mu =\frac{1}{\tan \theta }$

B)
$\mu =\frac{2}{\tan \theta }$

C)
$\mu =2\tan \theta$

D)
$\mu =\tan \theta$

• question_answer51) An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of $12\,m{{s}^{-1}}$ and the second part of mass 2 kg moves with $8\,m{{s}^{-1}}$ speed. If the third part flies off with $4\,m{{s}^{-1}}$ speed, then its mass is                                               [NEET 2013]

A)
3 kg

B)
5 kg

C)
7 kg

D)
17 kg

• question_answer52)  A system consists of three masses ${{m}_{1}},{{m}_{2}}$ and ${{m}_{3}}$ connected by a string passing over a pulley P. The mass ${{m}_{1}}$ hangs freely and ${{m}_{2}}$ and ${{m}_{3}}$ are on a   rough horizontal table (the coefficient of friction $=\mu$). The pulley is frictionless and of [NEET 2014] negligible mass. The downward acceleration of mass ${{m}_{1}}$ is (Assume,${{m}_{1}}={{m}_{2}}={{m}_{3}}=m$)

A)
$\frac{g(1-g\mu )}{9}$

B)
$\frac{2g\mu }{3}$

C)
$\frac{g(1-2\mu )}{3}$

D)
$\frac{g(1-2\mu )}{2}$

• question_answer53)  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      [NEET 2014] A)
24 Ns

B)
20 Ns

C)
12 Ns

D)
6 Ns

• question_answer54) 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?   [NEET 2014]

A)
$\frac{2ma}{g+a}$

B)
$\frac{2ma}{g-a}$

C)
$\frac{ma}{g+a}$

D)
$\frac{ma}{g-a}$

• question_answer55) A body of mass $(4\,w)$ is lying in $xy-$plane at rest. It suddenly explodes into three pieces. Two pieces each of mass (m) move perpendicular to each other with equal speeds $(\upsilon )$. The total kinetic energy generated due to explosion is [NEET 2014]

A)
$m{{v}^{2}}$

B)
$\frac{3}{2}m{{v}^{2}}$

C)
$2m{{v}^{2}}$

D)
$4\,m{{v}^{2}}$

• question_answer56)  Three blocks A, B and C of masses 4 kg, 2 kg   and 1 kg respectively, are in contact on a 1   frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is  [NEET 2015 ] A)
2 N

B)
6 N

C)
8 N

D)
18 N

• question_answer57) A block A of mass ${{m}_{1}}$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass ${{m}_{2}}$ is suspended. The coefficient of kinetic friction between the block and the table is ${{\mu }_{k}}$. When the block A is sliding on the table, the tension in the string is              [NEET 2015 ]

A)
$\frac{({{m}_{2}}+{{\mu }_{k}}{{m}_{1}})g}{({{m}_{1}}+{{m}_{2}})}$

B)
$\frac{({{m}_{2}}+{{\mu }_{k}}{{m}_{1}})g}{({{m}_{1}}+{{m}_{2}})}$

C)
$\frac{{{m}_{1}},{{m}_{2}}(1+{{\mu }_{k}})g}{({{m}_{1}}+{{m}_{2}})}$

D)
$\frac{{{m}_{1}}{{m}_{2}}(1-{{\mu }_{k}})g}{({{m}_{1}}+{{m}_{2}})}$

• question_answer58)  A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches ${{30}^{o}},$ the box starts to slip and slides m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively                    [NEET 2015 (Re)] A)
0.6 and 0.6

B)
0.6 and 0.5

C)
0.5 and 0.6

D)
0.4 and 0.3

• question_answer59) Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius $\frac{r}{2}$ and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value n is                                    [NEET 2015 (Re)]

A)
2

B)
3

C)
4

D)
1

• question_answer60)  The position vector of a particle R as a function of time is given by $\mathbf{R}=4\sin (2\pi t)\,\mathbf{\hat{i}}+4\cos (2\pi t)\,\mathbf{\hat{j}}$ where R is in metre, t is in seconds and $\mathbf{\hat{i}}$ and $\mathbf{\hat{j}}$ denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of particle? [NEET 2015 (Re)]

A)
Acceleration is along  R

B)
Magnitude of acceleration vector is $\frac{{{v}^{2}}}{R},$ where v is the velocity of particle

C)
Magnitude of the velocity of particle is $8\,m/s$

D)
Path of the particle is a circle of radius

• question_answer61) A nucleus of uranium decays at rest into nuclei of thorium and helium. Then,   [NEET 2015 (Re)]

A)
the helium nucleus has more kinetic energy than the thorium nucleus

B)
the helium nucleus has less momentum than the thorium nucleus

C)
the helium nucleus has more momentum than the thorium nucleus

D)
the helium nucleus has less kinetic energy than the thorium nucleus

• question_answer62) A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tang entail acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8\times {{10}^{4}}\text{ }J$ by the end of the second revolution after the beginning of the motion?        [NEET - 2016]

A)
$0.1\text{ }m/{{s}^{2}}$

B)
$0.15\text{ }m/{{s}^{2}}$

C)
$0.18\text{ }m/{{s}^{2}}$

D)
$0.2\text{ }m/{{s}^{2}}$

• question_answer63) 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 [NEET - 2016]

A)
$\sqrt{g{{R}^{2}}\frac{{{u}_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}$

B)
$\sqrt{gR\frac{{{u}_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}$

C)
$\sqrt{\frac{g}{R}\frac{{{u}_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}$

D)
$\sqrt{\frac{g}{{{R}^{2}}}\frac{{{u}_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}$

• question_answer64) A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k. Then they are connected in parallel and force constant is k. Then $k:k$ is     [NEET-2017]

A)
1 : 14

B)
1 : 6

C)
1 : 9

D)
1 : 11

• question_answer65) Which one of the following statements is incorrect?                                     [NEET - 2018]

A)
Frictional force opposes the relative motion.

B)
Limiting value of static friction is directly proportional to normal reaction.

C)
Rolling friction is smaller than sliding friction.

D)
Coefficient of sliding friction has dimensions of length.

• question_answer66)  A block of mass m is placed on a smooth inclined wedge ABC of inclination $\theta$ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and $\theta$ for the block to remain stationary on the wedge is  [NEET - 2018] A)
$a=g\,\,\cos \theta$

B)
$a=\frac{g}{\sin \theta }$

C)
$a=\frac{g}{\text{cosec}\theta }$

D)
$a=g\tan \theta$

• question_answer67)  A particle moving with velocity $\overrightarrow{V}$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will:           [NEET 2019] A)
Remain constant

B)
Change according to the smallest force $\overrightarrow{QR}$

C)
Increase

D)
Decrease

• question_answer68) A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when: [NEET 2019]

A)
The mass is at the lowest point

B)
Inclined at an angle of $60{}^\circ$ from vertical

C)
The mass is at the highest point

D)
The wire is horizontal

• question_answer69) When an object is shot from the bottom of a long smooth inclined plane kept at an angle$60{}^\circ$ with horizontal, it can travel a distance ${{x}_{1}}$along the plane. But when the inclination is decreased to $30{}^\circ$ and the same object is shot with the same velocity, it can travel ${{x}_{2}}$distance. Then ${{x}_{1}}:{{x}_{2}}$will be:                                                 [NEET 2019]

A)
$1:\sqrt{3}$

B)
$1:2\sqrt{3}$

C)
$1:\sqrt{2}$

D)
$\sqrt{2}:1$

• question_answer70) Two particles A and B are moving in uniform circular motion in concentric circles of radii ${{r}_{A}}$and ${{r}_{B}}$with speed ${{v}_{A}}$and ${{v}_{B}}$respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be: [NEET 2019]

A)
${{r}_{B}}:{{r}_{A}}$

B)
1 : 1

C)
${{r}_{A}}:{{r}_{B}}$

D)
${{v}_{A}}:{{v}_{B}}$

• question_answer71)  Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is: [NEET 2020] A)
g/2

B)
g/5

C)
g/10

D)
g

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