11.

Two masses M and M/2 are joined together by means of light inextensible string passed over a frictionless pulley as shown in the figure. When the bigger mass is released, the small one will ascend with an acceleration of

                        

• $\frac{\mathrm{g}}{3}$

• $\frac{3\mathrm{g}}{2}$

• $\frac{\mathrm{g}}{2}$

• g

In elastic collision

• both momentum and kinetic energies are conserved

• both momentum and kinetic energies are not conserved

• only energy is conserved

• only mechanical energy is conserved

A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is

• 1 : 2 : 3

• 1 : 4 : 9

• 1 : 3 : 5

• 1 : 5 : 3

When the kinetic energy of a body is doubled, its momentum increases by times

• $\sqrt{2}$

• 2

• 4

• $2\sqrt{2}$

Three identical spheres, each of mass 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

• $\frac{\mathrm{PQ}\hspace{0.17em}+ \mathrm{PR}\hspace{0.17em}+ \mathrm{QR}}{3}$

• $\frac{\mathrm{PQ}\hspace{0.17em}+ \mathrm{PR}}{3}$

• $\frac{\mathrm{PQ}\hspace{0.17em}+ \mathrm{QR}}{3}$

• $\frac{\mathrm{PR}\hspace{0.17em}+ \mathrm{QR}}{3}$

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

• $\frac{{\mathrm{ML}}^2}{6}$

• $\frac{{\mathrm{ML}}^2}{12}$

• $\frac{7{\mathrm{ML}}^2}{48}$

• $\frac{7{\mathrm{ML}}^2}{12}$

A body rolls down an inclined plane. If its kinetic energy of rotation is 40% of its kinetic energy of translation, then the body is

• solid cylinder

• solid sphere

• disc

• ring

Which of the following statements about the gravitational constant is true ?

• It is a force

• It has no unit

• It does not depend on the nature of the medium in which the bodies are kept

• It depends on the value of the masses

Four particles each of mass M, are located at the vertices of a square with side L. The gravitational potential due to this at the centre of the square is

• $-\sqrt{32} \frac{\mathrm{GM}}{\mathrm{L}}$

• $-\sqrt{64} \frac{\mathrm{GM}}{{\mathrm{L}}^2}$

• zero

• $\sqrt{32} \frac{\mathrm{GM}}{\mathrm{L}}$

Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to

• R²

• R^-2

• R⁴

• R^-4