A rocket is launched with velocity $10\, km/s$. If radius of earth is $R$, then maximum height attained by it will be

At what altitude in metre will the acceleration due to gravity be $25\%$ of that at the earth's surface (Radius of earth $= R\, metre$)

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 spherical planet has a mass $M$ and diameter $D$ . A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity , equal to  

The mass of a planet is $\frac{1}{10}^{\text {th }}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

Assuming the earth to be a sphere of uniform mass density, a body weighed $300 \mathrm{~N}$ on the surface of earth. How much it would weigh at $R / 4$ depth under surface of earth?