Earth is revolving around the sun. If the distance of the earth from the sun is reduced to 1/4th of the present distance then the length of present day will be reduced by :

• $\frac{1}{4}$

• $\frac{1}{2}$

• $\frac{1}{8}$

• $\frac{1}{6}$

52.

There are two planets and the ratio of radius of the two planets is K but ratio of acceleration due to gravity of both planets is g. What will be the ratio of their escape velocity ?

• (kg)^1/2

• (kg)^-1/2

• (kg)²

• (kg)^-2

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then

• g' = 3g

• $\mathrm{g}\text{'} = \frac{\mathrm{g}}{9}$

• g' = 9g

• g' = 27g

Two satellites of earth, S₁ and S₂ are moving in the same orbit. The mass of S₁ is four times the mass of S₂. Which one of the following statements is true ?

• The time period of S₁ is four times that of S₂

• The potential energies of earth and satellite in the two cases are equal

• S₁ and S₂ are moving with the same speed

• The kinetic energies of the two satellites are equal

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

• 2

• $\frac{1}{2}$

• $\frac{1}{\sqrt{2}}$

• $\sqrt{2}$

A satellite orbiting the earth in a circular orbit of radius R completes one revolution in 3h. If orbital radius of geostationary satellite is 36000 km, orbital radius of earth is

• 6000 km

• 9000 km

• 12000 km

• 15000 km

A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R. If the satellite is intended to move in a circular orbit of radius 7R, the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant= G)

• $\frac{\mathrm{GMm}}{\mathrm{R}}$

• $- \frac{13 \mathrm{G} \mathrm{M} \mathrm{m}}{14 \mathrm{R}}$

• $\frac{\mathrm{GMm}}{7\mathrm{R}}$

• $-\frac{\mathrm{G} \mathrm{M} \mathrm{m}}{14 \mathrm{R}}$

The escape velocity for the earth is 11.2 km/s. The mass of another planet 100  times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is

• 280 km/s

• 56.0 km/s

• 112 km/s

• 56 km/s

Change in acceleration due to gravity is same upto a height h from each other the earth surface and below depth x then relation between x and his ( h and x<<<R_e )

• x = h

• x = 2h

• x = $\frac{\mathrm{h}}{2}$

• x = h²

 A uniform ring of mass m and radius a is placed directly above a uniform sphere of mass m and of equal to radius. The centre of the ring is at a distance $\sqrt{3}$a from the centre of the sphere. The gravitational force (Fl exerted by the sphere on the ring is

• $\frac{\sqrt{3} \mathrm{G} \mathrm{Mm}}{8 {\mathrm{a}}^2}$

• $\frac{2 \mathrm{G} \mathrm{M} \mathrm{m}}{3 {\mathrm{a}}^2}$

• $\frac{7 \mathrm{G} \mathrm{Mm}}{\sqrt{2} {\mathrm{a}}^2}$

• $\frac{3 \mathrm{G} \mathrm{Mm}}{{\mathrm{a}}^2}$