A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be

If $v_e$ is escape velocity and $v_0$ is orbital velocity of satellite for orbit close to the earth's surface. Then these are related by

The mass of planet is $\frac{1}{9}$ of the mass of the earth and its radius is half that of the earth. If a body weight $9\,N$ on the earth. Its weight on the planet would be  ........ $N$

A planet orbits the sun in an elliptical path as shown in the figure. Let $v_P$ and $v_A$ be speed of the planet when at perihelion and aphelion respectively. Which of the following relations is correct ?

A satellite is orbitting around the earth with areal speed $v_a$. At what height from the  surface of the earth, it is rotating, if the radius of earth is $R$

If the radius of the earth were to shrink by $1\%$ its mass remaining the same, the acceleration due to gravity on the earth's surface would