11.

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 $\overline{\mathrm{v}{\text{'}}_2}$ at time 2t₀ while still moving in it. The value of $\left|\left({\mathrm{m}}_1\overline{\mathrm{v}\text{'}} + {\mathrm{m}}_2\overline{\mathrm{v}{\text{'}}_2}\right) - \left({\mathrm{m}}_1\overline{{\mathrm{v}}_1} + {\mathrm{m}}_2\overline{{\mathrm{v}}_2}\right)\right|$ is

• zero

• (m₁ + m₂) gt₀

• 2 (m₁ + m₂) gt₀

• $\frac{1}{2}\left({\mathrm{m}}_1 + {\mathrm{m}}_2\right) {\mathrm{gt}}_0$

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

• $\sqrt{2} \mathrm{Mg}$

• $\sqrt{2} \mathrm{mg}$

• $\sqrt{{\left(\mathrm{M}\hspace{0.17em}+ \mathrm{m}\right)}^2 + {\mathrm{m}}^2\mathrm{g}}$

• $\sqrt{{\left(\mathrm{M} + \mathrm{m}\right)}^2 + {\mathrm{M}}^2} \mathrm{g}$

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

• $\frac{5}{4} {\mathrm{mr}}^2$

• $\frac{5}{2} {\mathrm{mr}}^2$

• $\frac{1}{4} {\mathrm{mr}}^2$

• $\frac{1}{2} {\mathrm{mr}}^2$

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

• $\frac{6\mathrm{F}}{\mathrm{MR}}$

• $\frac{3\mathrm{F}}{\mathrm{MR}}$

• $\frac{6\mathrm{F}}{5\mathrm{MR}}$

• $\frac{4\mathrm{F}}{\mathrm{MR}}$

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

• ${\mathrm{v}}_0 = \sqrt{\mathrm{gh}}$

• ${\mathrm{v}}_0 = \sqrt{5\mathrm{gh}}$

• ${\mathrm{v}}_0 = \sqrt{2\mathrm{gh}}$

• 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 = $\left(7\stackrel{\wedge }{\mathrm{i}} - 6\stackrel{\wedge }{\mathrm{j}}\right)$ 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

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