The gravitational force between two point masses $m_1$ and $m_2$ at a separation $r$ is given by $F = k \frac{m_1 m_2}{r^2}$. The constant $k$:

Explain the vector form of Newton's universal law of gravitation.

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).

Two metallic spheres each of mass $M$ are suspended by two strings each of length $L$. The distance between the upper ends of the strings is $L$. The angle which the strings will make with the vertical due to the mutual attraction of the spheres is

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:

Two objects are placed at a certain distance from each other in air. If they are placed at the same distance in water,what is the ratio of the gravitational force between them?