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

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

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

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

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

The moment of inertia of a thin rod of mass M and length L, about an axis perpendicularto the rod at a distance $\frac{\mathrm{L}}{4}$from one end is

• $\frac{{\mathrm{ML}}^2}{6}$

• $\frac{{\mathrm{ML}}^2}{12}$

• $\frac{7 {\mathrm{ML}}^2}{24}$

• $\frac{7 {\mathrm{ML}}^2}{48}$

168.

If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take

• 96 h

• 48 h

• 6 h

• 1.5 h

A shell of mass 10 kg is moving with a velocity of 10 ms^-1 when it blasts and forms two parts of mass 9 kg and 1 kg respectively. If the 1^st mass is stationary, the velocity of the 2^nd is

• 1 m/s

• 10 m/s

• 100 m/s

• 1000 m/s

A circular disc rolls down on an inclined plane without slipping. What fraction of its total energy is translational ?