Gravitational Potential and Potential Energy

Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of the escape velocity  $\frac{{\text{V}}_{\text{A}}}{{\text{V}}_{\text{B}}}\text{is}$

Given that the gravitation potential on Earth surface is $V_0$. The potential at a point distant half the radius of earth from the centre will be

The gravitational potential energy of a system of three particles of mass $m$ each kept at the vertices of equilateral triangle of side $x$ will be

A particle is projected vertically upward with velocity $\sqrt{\frac{2GM}{3R}}$ from the surface of the Earth. The height attained by it is ($G,M,R$ have usual meanings)

Calculate the binding energy of an artificial satellite of mass $1000 kg$ orbiting at a height of $3600 km$ above the earth's surface. Also find the kinetic energy, potential energy, and total energy of the satellite. Given, $R=6400 km$, $M=6\times {10}^{24} kg$, $G=6.67\times {10}^{-11} \raisebox{1ex}{$N{m}^2$}\!\left/ \!\raisebox{-1ex}{$k{g}^2$}\right.$.

At what height above the surface of the earth, the value of g becomes $64\%$of its value on the surface is the earth? (Radius of the earth is $6400\mathrm{km}$ )

Which one of the following possesses potential energy

Which of the following is not an example of potential energy

Potential energy of a person is minimum when:

A body falls on the surface on the earth from a height of $20\mathrm{cm}.$ If after colliding with the earth, its mechanical energy is lost by $75\%,$ then body would reach upto a height of?

A missile is launched with a velocity less than the escape velocity. The sum of kinetic energy and potential energy is :

Define Gravitational potential energy. Derive an expression for the gravitation potential energy above the surface of the earth.

Two bodies each of mass $M$ are kept fixed with a separation $2L$. A particle of mass $m$ is projected from the mid-point of the line joining their centres perpendicular to the line. The gravitational constant is $G$. The correct statement $\left(s\right)$ is (are)

Three masses $m, 2 \mathrm{m}$ and $3 \mathrm{m}$ are arranged in two triangular configurations as shown in figure $1$ and figure $2$ . Work done by an external agent in changing the configuration from figure $1$ to figure $2$ is

The escape velocity of a spherical planet of radius $R$ and density $\rho$ is $V$. If the radius of this planet is changed to $3R$ and density is changed to $3\rho$, then the escape velocity of the planet will be changed to

Velocity of escape, from earth’s surface, is _____  $\mathrm{km} {\mathrm{s}}^{-1}$.

Calculate the escape velocity of a body from the surface of the earth. $(\mathrm{Given}: G=6.67 \mathrm{x} {10}^{-11} {\mathrm{Nm}}^2/{\mathrm{kg}}^2, R=6400 \mathrm{km}, g=9.8 \mathrm{m}/{\mathrm{s}}^2)$

Define escape velocity. Write an expression for the escape velocity of an object from the surface of the earth.

If any object is thrown upwards with a velocity more than $11.2 \mathrm{km}/\sec$, then the object will:

A spherical portion of radius $\frac{R}{2}$ is removed from a solid sphere of mass $M$ and radius $R$ as shown in the figure. Taking gravitational potential $V=0$ at $r=\infty$, the potential at the centre of the cavity thus formed is $(G=\text{gravitational constant})$,