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

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 geostationary satellite is orbiting the earth at a height of $6\,R$ above the surface of  earth ($R$ is the radius of earth). The time period of another satellite at a height of $2.5\,R$ from the surface of the earth is :-

If $R$ is the radius of earth and $g$ is the acceleration due to gravity on the earth's surface. Then mean density of earth is ..........

If the gravitational acceleration at surface of Earth is $g$, then increase in potential energy in lifting an object of mass $m$ to a height equal to half of radius of earth from surface will be

If the distance between centres of earth and moon is $D$ and the mass of earth is $81\, times$ the mass of moon, then at what distance from centre of earth the gravitational force will be zero