Gravitation - Mechanics - Physics Previous Year Questions

An object of mass $m$ at a distance of $20 R$ from the centre of a planet of mass $M$ and radius $R$ has an initity velocity $u$. The velocity with which the object hits the surface of the planet is

( $G$-Universal gravitational constant)

The ratio of the time periods of a simple pendulum at heights $2 R_E$ and $3 R_E$ from the surface of the Earth is ( $R_E$ is radius of the Earth)

If a body is projected vertically from the surface of the Earth with a speed of $8000 \mathrm{~ms}^{-1}$, then the maximum height reached by the body is

(Radius of the Earth $=6400 \mathrm{~km}$ and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If the orbital speed of a body revolving in a circular path near the surface of the Earth is $8 \mathrm{kms}^{-1}$, then the orbital speed of a body revolving around the Earth in a circular orbit at height of $19,200 \mathrm{~km}$ from the surface of Earth is (Radius of the Earth $=6400 \mathrm{~km}$ )

A body is projected from the Earth's surface with a speed $\sqrt{5}$ times the escape speed $\left(V_e\right)$. The speed of the body when it escapes from the gravitational influence of the Earth is

The force of mutual attraction between any two objects by virtue of their masses is

Which of the following is incorrect about the gravitational force between two bodies?

A meteor of mass ' $m$ ' having a speed ' $V$ ' at infinity reaches the surface of the Earth with a speed of ( $v_c$ is escape speed from the Earth's surface)