The mass of the moon is $1\%$ of the mass of the earth. The ratio of the gravitational pull of the earth on the moon and that of the moon on the earth will be

The distance between the centres of the moon and the earth is $D$. The mass of the earth is $81$ times the mass of the moon. At what distance from the centre of the earth will the net gravitational force on a test mass be zero?

State Newton's universal law of gravitation and represent it in a mathematical expression.

Three particles each of mass $m_{1}$ are placed at the corners of an equilateral triangle of side $\frac{L}{3}$. $A$ particle of mass $m_{2}$ is placed at the midpoint of any one side of the triangle. Due to the system of particles,the net gravitational force acting on $m_{2}$ is ($G$ = Universal constant of gravitation).

From a sphere of mass $M$ and radius $R$,a smaller sphere of radius $\frac{R}{2}$ is carved out. For the configuration shown in the figure where the distance between the center of the original sphere and the center of the removed sphere is $3R$,the gravitational force between the two spheres is:

$A$ straight rod of length $L$ extends from $x = a$ to $x = L + a$. The gravitational force it exerts on a point mass $m$ at $x = 0$,if the mass per unit length of the rod is $A + Bx^2$,is given by