B M Sharma Solutions for Chapter: Gravitation, Exercise 3: DPP 6.3

Three identical stars, each of mass $M,$ form an equilateral triangle (stars are positioned at the corners) that rotates around the centre of the triangle. The system is isolated and the edge length of the triangle is$L.$The amount of work done, that is required to dismantle the system is

Four particles each of mass $M$ are located at the vertices of a square with side length$L$. The gravitational potential due to this at the centre of the square is 

The gravitational field due to a mass distribution is $E=\frac{K}{x^2}$ in the$x-$direction. ($K$ is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance$x$is

A body of mass$m$ rises to height $h=\frac{R}{5}$ from the earth's surface, where $R$ is earth's radius. If $g$ is acceleration due to gravity at earth's surface, the increase in potential energy is

The escape velocity of a body of mass $1 \mathrm{kg}$ on a planet is $100 \mathrm{m} {\mathrm{s}}^{-1}$. Gravitational potential energy of the body at the planet is

For the moon to cease to remain in the earth's satellite, its orbital velocity has to increase by a factor of

The ratio of the radii of planets $A$ and $B$ is $k_1$ and ratio of acceleration due to gravity on them is $k_2$. The ratio of escape velocities from them will be $\sqrt{n{k}_1{k}_2}$. Value of $n$ is _____.

If the mass of the earth is $M$, radius is $R$ and gravitational constant is $G$, then work done to take $1 \mathrm{kg}$mass from the earth's surface to infinity will be