31.

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

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

• $\frac{{\mathrm{ML}}^2}{6}$

• $\frac{{\mathrm{ML}}^2}{12}$

• $\frac{7 {\mathrm{ML}}^2}{24}$

• $\frac{7 {\mathrm{ML}}^2}{48}$

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 has same value in all systems of units

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

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

A piece of ice is floating in a jar containing water. When the ice melts, then the level of water

• rises

• falls

• remains unchanged

• rises or falls

A wire of length L and area of cross-section A is stretched through a distance x metre by applying a force F along length, then the work done in this process is (Y is Young's modulus of the material)

• $\frac{1}{2} \left(\mathrm{A} . \mathrm{L}\right) \left(\frac{\mathrm{Yx}}{\mathrm{L}}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $\left(\mathrm{A} .\hspace{0.17em}\mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $2\left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $3 \left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

An ice box made of Styrofoam (Thermal conductivity = 0.01Jm^-1 s^-1 K^-1 ) is used to keep liquids cool. It has a total wall area including lid of 0.8 m and wall thickness of 2.0 cm. A bottle of water is placed in the box and filled with ice. If the outside temperature is 30°C the rate of flow of heat into the box is (in J-s^-1 )

• 16

• 14

• 12

• 10