Two particles of masses m1 and m2 in projectile motion have velocities v1 and v2 (v1 < v2) respectively at t = 0. They collide at time t0. Their velocities become and at time 2t0 while still moving in it. The value of is
zero
(m1 + m2) gt0
2 (m1 + m2) gt0
If the equation for the displacement of a particle moving on a circular path is given by θ = 2 t3+ 0.5, where θ is in radian and t in second, then the angular velocity of the particle after 2 s from its start is
8 rad/s
12 rad/s
24 rad/s
36 rad/s
A block of mass m is placed on a smooth inclined plane of inclination with the horizontal. The force exerted by the plane on the block has a magnitude
mg
mg/cos θ
mg cos θ
mg tan θ
A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by
The moment of inertia of a uniform ring of mass m and radius r about an axis, AA' touching the ring tangentially and lying in the plane of the ring only, as shown in figure, is
If the disc shown in figure has mass M and it is free to rotate about its symmetrical axis passing through O, its angular acceleration is
A small ball released from rest from a height h on a smooth surface of varying inclination, as shown in figure.
The speed of the ball when it reaches the horizontal part of the surface is
None of these
Two masses m1 = 5 kg and m2 = 4.8 kg tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move ?
0.2 m/s2
9.8 m/s2
5 m/s2
4.8 m/s2
A particle is acted upon by a conservative force F = N (no other force is acting on the particle). Under the influence of this force, particle moves from (0,0) to (-3m, 4m), then
work done by the force is 3 J
work done by the force is − 45 J
at (0, 0) speed of the particle must be zero
at (0, 0) speed of the particle must not be zero
B.
work done by the force is − 45 J
Work done of the particle
W = F . ds
=
= − 21 − 24
W = − 45 J
If W1 , W2 and W3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively in the gravitational field of a point mass m shown in the figure, find the correct relation between W1 , W2 and W3 .
W1 > W2 > W3
W1 = W2 = W3
W1 < W2 < W3
W2 > W1 > W3