11.

A solid sphere is set into motion on a rough horizontal surface with a linear speed v in the forward direction and an angular speed $\frac{\mathrm{v}}{\mathrm{R}}$ in the anticlockwise direction as shown in figure. Find the linear speed of the sphere when it stops rotating and ω = $\frac{\mathrm{v}}{\mathrm{R}}$

  

• $\frac{3\mathrm{v}}{5}$

• $\frac{2 \mathrm{v}}{5}$

• $\frac{4 \mathrm{v}}{3}$

• $\frac{7 \mathrm{v}}{3}$

Two blocks of masses m₁ and m₂ are connected by a spring of spring constant k. The block of mass m₂ is given a sharp empulse so that it acquires a velocity v₀ towards right. Find the maximum elongation that the spring will suffer.

• ${\left[\frac{{\mathrm{m}}_1 {\mathrm{m}}_2}{{\mathrm{m}}_1 + {\mathrm{m}}_2}\right]}^{\frac{1}{2}}$ v₀

• $\left(\frac{{\mathrm{m}}_1 + {\mathrm{m}}_2}{{\mathrm{m}}_1 - {\mathrm{m}}_2}\right)$v₀

• ${\left[\frac{{\mathrm{m}}_1 + {\mathrm{m}}_2}{{\mathrm{m}}_1 - {\mathrm{m}}_2}\right]}^{\frac{1}{2}}$ v₀ 

• ${\left[\frac{2{\mathrm{m}}_1 + {\mathrm{m}}_2}{{\mathrm{m}}_1 {\mathrm{m}}_2}\right]}^{\frac{1}{2}}$ v₀

A ball of mass m hits the floor with a speed v making an angle of incidence θ with the normal. The coefficient of restitution is e. The speed of reflected ball and the angle of reflection of the ball will be

• v' = v, θ = θ'

• v' = $\frac{\mathrm{v}}{2}$, θ = 2θ'

• v' = 2v, θ = 2θ'

• v' = $\frac{3\mathrm{v}}{2}, \mathrm{\theta } = \frac{2\mathrm{\theta }\text{'}}{3}$

A particle slides on surface of a fixed smooth sphere starting from top most point. The angle rotated by the radius through the particle, when it leaves contact with the sphere, is

• $\mathrm{\theta } ={\cos }^{-1} \frac{1}{3}$

• $\mathrm{\theta } = {\cos }^{-1} \left(\frac{2}{3}\right)$

• $\mathrm{\theta } = {\tan }^{-1} \left(\frac{1}{3}\right)$

• $\mathrm{\theta } = {\sin }^{-1} \frac{4}{3}$

What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle θ/2 with the horizontal?

A block of mass 2 kg is pushed against a  rough vertical wall with a force of 40 N, coefficient of static friction being 0.5. Another horizontal force of 15 N, is applied
on the block in a direction parallel to the wall. If the block will move, then its direction would be

• 15^o with 15 N force

• 53^o with 15 N force

• 45^o with 15 N force 

• 75^o with 15N force

A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/s². Find the displacement of the block during the first 0.2 s after the start. (Take, g = 10 m/s²)

• 30 cm

• zero

• 20 cm

• 25 cm

A monkey of mass 15 kg is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration 1 m/s, how much force should it apply to the rope if rope is 5 m long and the monkey starts from rest?

• 150 N

• > 160 N

• 165 N

• 150 < T ≤ 160 N

A body weighing 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is

• 13 g

• 9 g

• 22 g

• 12 g

A rod PQ of length l is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end Q is 2 m/s towards negative direction of x. The speed of end P will be

• $\sqrt{3} {\mathrm{ms}}^{-1}$

• $\frac{2}{\sqrt{3}} {\mathrm{ms}}^{-1}$

• $\sqrt{2} {\mathrm{ms}}^{-1}$

• $\frac{\sqrt{5}}{2} {\mathrm{ms}}^{-1}$