If a thin uniform wire of length X having linear mass density D is bent zero into a circular loop (as shown in the figure). What will be the moment of inertia of the loop about axis AB ?

• 3 L²D/ 16 $\mathrm{\pi }$

• 2 L²D/ 3$\mathrm{\pi }$

• 3 L³D/ 8${\mathrm{\pi }}^2$

• 8 L²D/ 13${\mathrm{\pi }}^2$

A solid sphere rolls without slipping and presses a spring of spring constant k as shown in figure. Then, the compression in the spring will be

• $\sqrt{\frac{2\mathrm{M}}{3\mathrm{k}}}$

• $\sqrt{\frac{2\mathrm{M}}{5\mathrm{k}}}$

• $\sqrt{\frac{5\mathrm{k}}{7\mathrm{M}}}$

• $\sqrt{\frac{7\mathrm{m}}{5\mathrm{k}}}$

243.

A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 ms^-2, then the maximum angular velocity of the stone will be

• 2 rad s^-1

• 4 rad s^-1

• 8 rad s^-1

• 16 rad s^-1

A force-time graph for a linear motion of a body is shown in the figure. The change in linear momentum between O and 7 s is

• 2 N-s

• 3 N-s

• 4 N-s

• 5 N-s

Two blocks of equal masses m are released from the top of a smooth fixed wedge as shown in the figure. The acceleration of the centre of mass of the two blocks is

• g

• $\frac{\mathrm{g}}{2}$

• $\frac{3\mathrm{g}}{4}$

• $\frac{\mathrm{g}}{\sqrt{2}}$

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge ofthe disc and normal to the disc is

• MR²

• $\frac{1}{2}{\mathrm{MR}}^2$

• $\frac{3}{2}{\mathrm{MR}}^2$

• $\frac{7}{2}{\mathrm{MR}}^2$

Moment of a couple is called

• impulse

• couple

• torque

• angular momentum

A motor is rotating at a constant angular velocity of 500 rpm. The angular displacement per second is 

• $\frac{3}{50 \mathrm{\pi }} \mathrm{rad}$

• $\frac{3\mathrm{\pi }}{50} \mathrm{rad}$

• $\frac{25 \mathrm{\pi }}{3} \mathrm{rad}$

• $\frac{50 \mathrm{\pi }}{3} \mathrm{rad}$

If the length of the second's hand in a stop-clock is 3 cm, the angular velocity and linear velocity of the tip is

• 0.2047 rad/s , 0.0314 ms^-1

• 0.2547 rad/s , 0.314 ms^-1

• 0.1472 rad/s , 0.06314 ms^-1

• 0.1047 rad/s , 0.00314 ms^-1

Three identical spheres, each ofmass 1 kg are kept as shown in figure below, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is

• $\frac{\mathrm{PQ} + \mathrm{PR} + \mathrm{QR}}{3}$

• $\frac{\mathrm{PQ} + \mathrm{PR}}{3}$

• $\frac{\mathrm{PQ} + \mathrm{QR}}{3}$

• $\frac{\mathrm{PR} + \mathrm{QR}}{3}$