Gravitational Potential of a Solid Sphere

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

1. $-\frac{GM}{2R}$
2. $-\frac{GM}{R}$
3. $-\frac{2GM}{3R}$
4. $-\frac{2GM}{R}$

Q. The potential at any internal point of earth at a distance r from the centre is $\frac{-GM}{2R^3}(3R^2-r^2)$.

1. False
2. True

Q. A sphere of uniform density has a spherical cavity inside it, then

1. field inside cavity will be constant.
2. region of cavity may be equipotential.
3. region of cavity may not be equipotential.
4. field inside cavity may be zero.

Q. From a solid sphere of mass $M$ and radius $R$, a spherical portion of radius $\left(\frac{R}{2}\right)$ is removed 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 = gravitational constant)

1. $-\frac{GM}{R}$
2. $-\frac{GM}{2R}$
3. $-\frac{-2GM}{3R}$
4. $-\frac{-2GM}{R}$

Q. Figure shows the variation of kinetic energy, potential energy and total energy as a function of the radius of a body in circular motion. Then

1. A, B, C represent total energy, kinetic energy and potential energy respectively.
2. A, B, C represent kinetic energy, potential energy and total energy respectively.
3. A, B, C represent kinetic energy, total energy and potential energy respectively.
4. A, B, C represent potential energy, kinetic energy and total energy respectively.

Q. If the potential at the surface of a planet of mass M and radius R is assumed to be zero. Then the potential at infinity is.

1. $\frac{GM}{R}$
2. $\frac{\_GM}{R}$
3. not defined.
4. zero

Q. A diametrical tunnel is dug across earth. A ball is dropped into tunnel from one side. The velocity of the ball when it reaches other en​​​d is.​

1. $\sqrt{0.5gR}$
2. $\sqrt{gR}$
3. $\sqrt{2gR}$
4. zero