Question

A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a. The centre of the shell falls on the surface of the inner sphere

• A. The gravitational potential at $P_2=0$
• B. The gravitational field intensity at $P_2$ is $\frac{61GM}{900a^2}$
• C. The gravitational field intensity at $P_1$ is $\frac{GM}{16a^2}$
• D. The gravitational potential at $P_1=0$

Answer 1

Answer: (B), (C)

The gravitational field intensity at $P_1$ is $\frac{GM}{16a^2}$

$E_{P_1}=\frac{GM}{{\left(4a\right)}^2}=\frac{GM}{16a^2}$

$E_{P_2}=\frac{GM}{{\left(6a\right)}^2}+\frac{GM}{5a^2}=\frac{61GM}{900a^2}$