If the earth is treated as a sphere of  radius R and mass M, its angular momentum about the axis of rotation with period T, is

• $\frac{\mathrm{M} {\mathrm{R}}^2 \mathrm{T}}{2\mathrm{\pi }}$

• $\frac{4\mathrm{\pi } \mathrm{M} {\mathrm{R}}^2}{5\mathrm{T}}$

• $\frac{\mathrm{\pi } \mathrm{M} {\mathrm{R}}^3}{\mathrm{T}}$

• $\frac{2\mathrm{\pi } \mathrm{M} {\mathrm{R}}^2}{\mathrm{T}}$

Two particles are seen to collide and move jointly together after the collision. During such a collision, for the total system.

• both the mechanical energy and the linear momentum are conserved

• linear momentum is conserved but not the mechanical energy

• neither the mechanical energy nor the linear momentum is conserved

• mechanical energy is conserved but not the linear momentum

A body weighed 250 N on the surface assuming the earth to be a sphere of uniform mass density, how much would it weigh halfway down to the centre of the earth?

• 195 N

• 240 N

• 125 N

• 210 N

What is the dimensional formula for the gravitational constant?

• [ M^-1 L³ T^-2 ]

• [ M^-1 L³ T^-1 ]

• [ M^-2 L³ T^-2 ]

• [ M^-2 L^-1 T³ ]

The equivalent resistance between A and C of the given circuit, is

• 8 Ω

• $\frac{32}{14} \mathrm{\Omega }$

• $\frac{4}{3}$Ω

• $\frac{8}{3}$Ω

Assertion:  Centripetal force does no work. 

Reason:  Force and displacement are perpendicular to each other.

• If both assertion and  reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If assertion is false but reason is true.

Assertion: Work done in uniform circular motion is zero.

Reason:  Force is always directed along displacement.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If assertion is false but reason is true.

Assertion:  At pole value of acceleration due to gravity (g) is greater than that of equator. 

Reason:  Earth rotates on its axis in addition to revolving round the sun.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true and reason is not the correct expalnation of assertion.

• If assertion is true but reason is false.

• If assertion is false and reason is true.

Assertion: The time period of revolution of a satellite around a planet is directly proportional to the radius of the orbit of the satellite.

Reason:  Artificial satellite do not follow Kepler's laws of planatary motion.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion is true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If assertion is false but reason is true.

20.

An engine is working. It takes 100 calories of heat from source and leaves 80 calories of heat to sink. If the temperature of source is 127°C, then temperature of sink is

• 147°C

• 47°C

• 100^°C

• 47 K