What is the work done by the force of gravity in the following cases?
$(a)$ $A$ satellite moving around the Earth in a circular orbit of radius $35000 \, km$.
$(b)$ $A$ stone of mass $250 \, g$ is thrown up to a height of $2.5 \, m$.

(N/A) The work done is $0 \, J$. In a circular orbit,the force of gravity acts perpendicular to the direction of motion (displacement). Since the angle between force and displacement is $90^{\circ}$,the work done $W = F \cdot s \cdot \cos(90^{\circ}) = 0$.
$(b)$ Given: mass $m = 250 \, g = 0.25 \, kg$,height $h = 2.5 \, m$,acceleration due to gravity $g = 9.8 \, m/s^2$ (or $10 \, m/s^2$).
Since the stone is thrown upwards,the force of gravity acts downwards (opposite to displacement).
Work done $W = -mgh = -(0.25 \, kg) \times (9.8 \, m/s^2) \times (2.5 \, m) = -6.125 \, J$ (or $-6.25 \, J$ if $g = 10 \, m/s^2$ is used).