Gravitational Potential Energy and Gravitational Potential

The escape velocity for a planet is $V_e$. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

Two bodies of mass $m$ and $9m$ are placed at a distance $R$. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ($G=$gravitational constant):

Four spheres each of mass $m$ form a square of side $d$ (as shown in figure). A fifth sphere of mass $M$ is situated at the centre of square. The total gravitational potential energy of the system is :

A sphere of radius $10 \mathrm{cm}$ and mass ${10}^5 \mathrm{kg}$ has a uniform mass distribution. A mass of ${10}^3 \mathrm{kg}$  is moved from a point $A$ to $B$ as shown in fig. The amount of work done is$\left(\mathrm{G}=6.6\times {10}^{-11}{\mathrm{N} \mathrm{m}}^2{ \mathrm{kg}}^{-2}\right)$ 

A body of mass $m$ is placed on the earth's surface. It is taken from the earth's surface to a height $h=3R$ when $R$ is the radius of the earth. The change in gravitational potential energy of the body is

Which of the following most closely depicts the correct variation of the gravitation potential, $V\left(r\right)$ with distance $r$ due to a large planet of radius $R$ and uniform mass density? (figures are not drawn to scale)

What is intensity of gravitational field at the centre of a spherical shell -

A thin uniform angular disc (see figure) of mass $M$ has outer radius $4R$ and inner radius $3R$. The work required to take a unit mass from the point $P$ on its axis to infinity is

Which of the following is true about the gravitational potential $V$ due to a point mass at a distance $r$ from the point mass?

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

Escape velocity from the surface of a planet is $v_e.$ A tunnel is dug across the diameter of the planet and a ball is dropped into it. When the body reaches the centre of the planet, its speed is

Work done by the gravitational force to bring mass $m$ from $nR$ height from earth's surface to earth's surface slowly is $(R$ is radius of earth$)$

A body of mass $\mathrm{m}$ is lifted up from the surface of earth to a height three times the radius of the earth. The change in potential energy of the body is

Two uniform solid spheres of equal radii $R\text{,}$ but mass $M$ and $4M$ have a centre to centre separation $6R\text{,}$ as shown in the figure. A projectile of mass $m$ is projected from the surface of the sphere of mass $M$ directly towards the centre of the second sphere. The minimum speed of the projectile so that it reaches the surface of the second sphere is

A graph of kinetic energy $K$ of an asteroid versus $\frac{1}{r}$ (where $r$ is the distance from the centre of the planet $A$) is shown in the figure. Asteroid falls directly towards the centre of the planet $A$. What is the value of mass of the asteroid? ($M$ is the mass of planet $A, G$ is universal gravitational constant in SI units)

Two planets have the same mass, $M$. Each planet has a constant density, but the density of planet $2$ is twice as high as that of planet $1$. Identical objects of mass $m$ are placed on the surfaces of the planets. What is the relationship of the gravitational potential energy, $U_1$ on planet 1 to $U_2$ on planet $2$?

The gravitational potential energy is maximum at

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 $(G=\text{gravitational constant})$,

What is the gravitational potential on the surface of a uniform spherical shell of radius $R$ and mass $3m$ if a particle of mass $m$ is placed at the centre of the sphere?

Two spheres each of mass $\mathrm{M}$ and radius $\mathrm{R}$ are separated by a distance of $\mathrm{r}$ .If a line is joined in between the centres of the spheres, The gravitational potential at the midpoint of that line is