Gravitation practice · Mixed difficulty

A mass of $3 \times {10^{24}}\,kg$ is to be compressed in a sphere in such a way that the escape velocity from the sphere is $9 \times {10^8}\,m/s.$ Radius of the sphere should be $\left[ {G = 6.67 \times {{10}^{ - 11}}\,N{m^2}/k{g^2}} \right]$

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to

A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy

A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is:

A clock S is based on oscillation of a spring and a clock P is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius

If earth were to suddenly contract to half its present size, without change in its mass, the duration of the day will be

When a body is taken from the equator to the poles, its weight

The velocity with which a projectile must be fired so that it escapes Earth's gravitation does not depend on

The gravitational field due to a uniform solid sphere of mass $M$ and radius $a$ at the centre of the sphere is

What should be the period of rotation of earth so as to make any object on the equator weigh half of its present value?

Assertion: For a satellite revolving very near to earth's surface the time period of revolution is given by $1 \mathrm{~h} \, 24 \mathrm{~min}$.
Reason: The period of revolution of a satellite depends only upon its height above the earth's surface.

The centripetal force acting on a satellite orbiting round the earth and the gravitational force of earth acting on the satellite both equal $F$. The net force on the satellite is

Pertaining to two planets, the ratio of escape velocities from respective surfaces is $1: 2$, the ratio of the time period of the same simple pendulum at their respective surfaces is $2: 1$ (in same order). Then the ratio of their average densities is

Earth orbiting satellite will escape, if

For a body to escape from earth, angle at which it should be fired is?