Question

Two spherical shells have mass $m$ and $2m$ as shown. Choose the correct options

• A. Between A and B gravitational field strength is zero
• B. Between A and B gravitational potential is constant
• C. There will be two points one lying between Band C and other lying between C and infinity where gravitational field strength are same
• D. There will be a point between Band C where gravitational potential will be zero

Answer 1

Answer: (A), (B), (C)

The correct options are
A Between A and B gravitational field strength is zero
B Between A and B gravitational potential is constant
C There will be two points one lying between Band C and other lying between C and infinity where gravitational field strength are same

The superposition principle states that the field or potential at any point is the sum of the contributions to the field or potential respectively by the individual masses.

Any point between A and B is inside both the shells, so field is zero in between A and B and potential is constant between A and B.

Between B and C, field is due to the inner shell only whereas between C and infinity the field is due to both the shells (as if all the mass were present at the centre, A). So there will be a point between B and C and a point between C and infinity where field strengths are same. We have, for equality of field strengths:

$\frac{m}{r_{B-C}^2}=\frac{3m}{r_{C-\infty }^2}\Rightarrow r_{C-\infty }=\sqrt{3}{r}_{B-C}$

Options A, B and C are correct.