When a body is taken from pole to the equator its weight

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 particle of mass $m$ is placed at the centre of a uniform spherical shell of mass $3\,m$ and radius $R$. The gravitational potential on the surface of the shell is

A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. ($v_e$ is escape velocity and $k < 1$). If air resistance is considered to be negligible then the maximum height from the centre of earth to whichit can go, will be : ($R =$ radius of earth)

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

A satellite is moving around the earth with speed $V$ in circular orbit of radius $r$ . If the orbital radius is decreased by $2\%$ , the speed of the satellite will