Assuming the earth to be a sphere of uniform mass density, a body weighs $300 \,N$ on the surface of the earth. How much would it weigh at a depth of $R/4$ below the surface of the earth (in $\,N$)?

Define acceleration due to gravity. Give the magnitude of $g$ on the surface of earth.

At a height of $10 \,km$ above the surface of the earth,the value of acceleration due to gravity is the same as that at a particular depth below the surface of the earth. Assuming uniform mass density for the earth,the depth is ............. $km$.

The mass and diameter of a planet are twice those of earth. The period of oscillation of a pendulum on this planet will be (if it is a second's pendulum on earth).

The mass of a spherical planet is $4$ times the mass of the earth, but its radius $(R)$ is the same as that of the earth. How much work is done in lifting a body of mass $5 \,kg$ through a distance of $2 \,m$ on the planet (in $\,J$)? (Take $g = 10 \,ms^{-2}$ for Earth)

$A$ body weighs $72 \ N$ on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth (in $N$)?