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question_answer1)
Two small spheres each of mass m connected by a string of length \[2l\] are kept on a smooth horizontal surface. A vertical force F is applied at the middle of the string. What is maximum value of F for which the spheres do not lose contact with the surface?
A)
\[2mg\] done
clear
B)
\[mg\] done
clear
C)
\[\frac{3mg}{2}\] done
clear
D)
\[4mg\] done
clear
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question_answer2)
A particle of mass m is at rest at the origin at time \[t=0\]. It is subjected to a force \[F(t)={{F}_{0}}{{e}^{-bt}}\]in the \[x\] direction. Its speed \[v(t)\] is depicted by which of the following curves?
A)
B)
C)
D)
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question_answer3)
Figure shows the variation of force acting on a body with time. Assuming the body to start from rest, the variation of its momentum with time is best represented by which plot?
A)
B)
C)
D)
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question_answer4)
A 15 kg block is initially moving along a smooth horizontal surface with a speed of \[v=4\,m/s\] to the left. It is acted by a force \[F\], which varies in the manner shown. Determine the velocity of the block at \[t=15\] seconds.
Given that, \[F=40\cos \left( \frac{\pi }{10} \right)t\]
A)
12.5 m/s done
clear
B)
8.5 m/s done
clear
C)
20 m/s done
clear
D)
9.5 m/s done
clear
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question_answer5)
Two wooden blocks are moving on a smooth horizontal surface such that the mass \[m\] remains stationary with respect to the block of mass M as shown in the figure. The magnitude of force \[p\]is
A)
\[(M+m)g\,tan\,\beta \] done
clear
B)
\[g\,\tan \,\beta \] done
clear
C)
\[mg\,\cos \,\beta \] done
clear
D)
\[(M+m)g\,\cos ec\,\beta \] done
clear
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question_answer6)
A bullet of mass w moving with velocity \[{{v}_{0}}\]hits a wooden plank \[A\] of mass \[M\] placed on a smooth horizontal surface. The length of the plank is \[\ell \]. The bullet experiences a constant resistive force F inside the block. The minimum value of \[{{v}_{0}}\] such that it is able to come out of the plank is
A)
\[\sqrt{\frac{F\ell /m}{{{M}^{2}}}}\] done
clear
B)
\[\begin{align} & \sqrt{\frac{2F\ell \,(M+m)}{Mm}} \\ & \\ \end{align}\] done
clear
C)
\[\begin{align} & \sqrt{\frac{2F\ell \,m}{{{M}^{2}}}} \\ & \\ \end{align}\] done
clear
D)
\[\sqrt{\frac{F\ell \,(M+m)}{M{{m}^{{}}}}}\] done
clear
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question_answer7)
A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be
A)
\[F\] done
clear
B)
\[2\,F/3\] done
clear
C)
\[3\,F/5\] done
clear
D)
\[5\,F/6\] done
clear
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question_answer8)
A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end. If a sudden jerk is given to C, then
A)
the portion AB of the string will break done
clear
B)
the portion BC of the string will break done
clear
C)
none of the strings will break done
clear
D)
the mass will start rotating done
clear
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question_answer9)
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
A)
\[mg\,\cos \,\theta \] done
clear
B)
\[mg\,\sin \,\theta \] done
clear
C)
\[mg\] done
clear
D)
\[mg/\,\cos \,\theta \] done
clear
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question_answer10)
A U-shaped wire has a rough semicircular bending between \[A\] and \[B\] as shown in the figure. \[A\] bead of mass m moving with uniform speed \[v\] through the wire enters the semicircular bend at \[A\] and leaves at \[B\] with velocity \[v/2\]after time \[T\]. The average force, exerted by the bead on the part \[A\]\[B\] of the wire is
A)
\[\frac{mv}{2T}\] done
clear
B)
\[\frac{3mv}{2T}\] done
clear
C)
\[\frac{3mv}{T}\] done
clear
D)
None of these done
clear
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question_answer11)
Two identical small masses each of mass m are connected by a light inextensible string on a smooth m horizontal floor. A constant force F is applied t at the mid point of the string as shown in the figure. The acceleration of each mass 1 towards each other is,
A)
\[\frac{F}{2\sqrt{3m}}\] done
clear
B)
\[\frac{\sqrt{3}F}{2m}\] done
clear
C)
\[\frac{2}{\sqrt{3}}\,\frac{F}{m}\] done
clear
D)
None of these done
clear
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question_answer12)
A wooden box is placed on a table. The normal force on the box from the table is A \[{{N}_{1}}\]. Now another identical box is kept on first box and the normal force on lower block due to upper block is A\[{{N}_{2}}\] and normal force on lower block by the table is \[{{N}_{3}}\]. For this situation, mark out the correct statement(s).
A)
\[{{N}_{1}}={{N}_{2}}={{N}_{3}}\] done
clear
B)
\[{{N}_{1}}<{{N}_{2}}={{N}_{3}}\] done
clear
C)
\[{{N}_{1}}={{N}_{2}}>{{N}_{3}}\] done
clear
D)
None of these done
clear
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question_answer13)
A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination \[30{}^\circ \] with horizontal. The acceleration of train up the plane is \[a\,=\,g/2\]. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium is
A)
\[30{}^\circ \] done
clear
B)
\[{{\tan }^{-1}}(2\sqrt[{}]{3})\] done
clear
C)
\[{{\tan }^{-1}}(\sqrt[{}]{3}/2)\] done
clear
D)
\[{{\tan }^{-1}}(2)\] done
clear
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question_answer14)
A bead of mass m is attached to one end of a spring of natural length R and spring constant\[k=\frac{(\sqrt{3}+1)mg}{R}\] The other end of the spring is fixed at a point A on a smooth vertical ring of radius R as shown in the figure. The normal reaction at B just after it is released to move is
A)
\[mg/2\] done
clear
B)
\[\sqrt{3\,}mg\] done
clear
C)
\[3\sqrt{3\,}mg\] done
clear
D)
\[\frac{3\sqrt{3}mg}{2}\] done
clear
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question_answer15)
A light string passing over a smooth light pulley connects two blocks of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] (vertically). If the acceleration of the system is g/8, then the ratio of the masses is
A)
8 : 1 done
clear
B)
9 : 7 done
clear
C)
4 : 3 done
clear
D)
5 : 3 done
clear
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question_answer16)
The figure shows the position-time \[(x-t)\] graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
A)
0.4 Ns done
clear
B)
0.8 Ns done
clear
C)
1.6Ns done
clear
D)
0.2 Ns done
clear
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question_answer17)
The system starts from rest and \[A\] attains a velocity of 5 m/s after it has moved 5 m towards right. Assuming the arrangement to be frictionless everywhere and pulley and strings to be light, the value of the constant force \[F\] applied on A is
A)
50 N done
clear
B)
75 N done
clear
C)
100 N done
clear
D)
96 N done
clear
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question_answer18)
A light spring balance hangs from the hook of the other light spring balance and a block of mass M kilogram hangs from the former one. Which of the following statements about the scale reading is true?
A)
Both the scales read \[M/2\] kilogram each. done
clear
B)
Both the scales read \[M\] kilogram each. done
clear
C)
The scale of the lower one reads \[M\] kilogram and of the upper one zero. done
clear
D)
The reading of the two scales can be anything but the sum of the reading will be \[M\] kilogram. done
clear
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question_answer19)
Initially the spring is undeformed. Now the force \[F\] is applied to \[B\] as shown in the figure. When the displacement of \[B\] w.r.t. \[A\] is x towards right in some time then the relative acceleration of \[B\] w.r.t. \[A\] at that moment is
A)
\[\frac{F}{2m}\] done
clear
B)
\[\frac{F-kx}{m}\] done
clear
C)
\[\frac{F-2kx}{m}\] done
clear
D)
None of these done
clear
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question_answer20)
An object is suspended from a spring balance in a lift. The reading is 240 N when the lift is at rest. If the spring balance reading now changes to 220 N, then the lift is moving
A)
Downward with constant speed done
clear
B)
Downward with decreasing speed done
clear
C)
Downward with increasing speed done
clear
D)
Upward with increasing speed done
clear
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question_answer21)
A machine gun fires a bullet of mass 40 g with a velocity \[1200m{{s}^{-1}}\]. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
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question_answer22)
Five forces \[{{\vec{F}}_{1}},{{\vec{F}}_{2}},{{\vec{F}}_{3,}}{{\vec{F}}_{4}},\,and\,{{\vec{F}}_{5}}\] are acting on a particle of mass 2.0 kg so that it is moving with \[4\,m/{{S}^{2}}\] in east direction. If \[{{\vec{F}}_{1}}\] force is removed, then the acceleration becomes \[7\,m/{{S}^{2}}\] in north, then the acceleration of the block if only \[{{\vec{F}}_{1}}\] is acting will be \[\sqrt{N}\,m/{{s}^{2}}\]. Find the value of n.
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question_answer23)
A rope is stretched between two boats at rest. A sailor in the first boat pulls the rope with a constant force of 100 N. First boat with the sailor has a mass of 250 kg whereas the mass of second boat is double of this mass. If the initial distance between the boats was 120 m, the time taken for two boats to meet each other is (neglect water resistance between boats and water) _____ s.
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question_answer24)
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 \[3\,\,m/{{s}^{2}}\] in east direction. When person A stops pulling, it moves with acceleration \[1\,\,m/{{s}^{2}}\] in the west direction. When person B stops pulling, it moves with acceleration \[24\,\,m/{{s}^{2}}\] in the north direction. What is the magnitude of acceleration in \[(m/{{s}^{2}})\] of the cart when only A and B pull the cart keeping their directions same as the old directions?
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question_answer25)
For the pulley system shown in the figure, each of the cables at A and B is given a velocity of \[2\,m{{s}^{-1}}\] in the direction of the arrow. Determine the upward velocity v in \[(m/{{s}^{{}}})\] of the load m.
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