A particle of mass $10\, g$ is kept of the surface of a uniform sphere of mass $100\, kg$ and a radius of $10\, cm .$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere. (you make take $\left.G=6.67 \times 10^{-11} Nm ^{2} / kg ^{2}\right)$

Mass of moon is $7.34 \times {10^{22}}\,kg$. If the acceleration due to gravity on the moon is $1.4\,m/{s^2}$, the radius of the moon is $(G = 6.667 \times {10^{ - 11}}\,N{m^2}/k{g^2})$

The acceleration due to gravity about the earth's surface would be half of its value on the surface of the earth at an altitude of ......... $mile$. ($R = 4000$ mile)

The weight of a body on the surface of the earth is $100\,N$. The gravitational force on it when taken at a height, from the surface of earth, equal to onefourth the radius of the earth is $..........\,N$

A person whose mass is $100\, {kg}$ travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as $10$ ${m} / {s}^{2}$ and $4 \,{m} / {s}^{2}$ respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

A body weights $49\,N$ on a spring balance at the north pole. ..... $N$ will be its weight recorded on the same weighing machine, if it is shifted to the equator?

(Use $g=\frac{G M}{R^{2}}=9.8 \,ms ^{-2}$ and radius of earth, $R =6400\, km .]$