Gravitational Field Due to a Shell

Q. A point mass m is situated inside a thick spherical shell of mass M, inner radius R and outer radius 2R. Work required to take this mass m from inside the shell to infinity, slowly is

1. $\frac{GMm}{2R}$
2. $\frac{7GMm}{15R}$
3. $\frac{9GMm}{14R}$
4. $\frac{3GMm}{7R}$

Q. Consider two satellites, $S_1$ and $S_2$ with periods of revolution, $1\text{hr}$ and $8\text{hr}$ respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite $S_1$ to the angular velocity of satellite $S_2$ is

1. $1:2$
2. $1:8$
3. $8:1$
4. $2:1$

Q. The intensity of gravitational field at the centre of a uniform spherical shell is .

1. $\frac{Gm}{r^2}$
2. zero
3. not defined

Q. Which one of the following plots represents the variation of gravitational field on a particle with distance $r$ due to a thin spherical sheet of radius $R$ ? ($r$ is measured from the centre of the spherical shell)

1. 
2. 
3. 
4. 

Q. The intensity of gravitational field at the centre of a uniform spherical shell is .

1. $\frac{Gm}{r^2}$
2. zero
3. not defined