A body of mass  $m$  falls from a height  $R$  above the surface of the earth, where $R$  is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$ )

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

The height at which the weight of a body becomes $\frac{1}{9} ^{th}$ its weight on the surface of earth (radius of earth is $R$)

Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively, measured from the centre of mass of the system. The magnitude of gravitational force $m_1$ exerts on $m_2$ is

A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R =$ Earth's radius)