Question

Potential due to uniform spherical shell of mass ' m' and radius R at a point inside it is​

Answer 1

To find:

Gravitational potential due to a uniform spherical shell of mass m and radius R at a point inside it is ?

Calculation:

We know that a spherical shell doesn't include any mass . Applying the concept of Gauss' Theorem (analogous to Electrostatics) , we can say that the gravitational field intensity inside the shell will be zero.

Now, let potential be V :

$\displaystyle \therefore \: \int dV = \int E \: dr$

$\displaystyle \implies \: \int_{V_{0}}^{V} dV = \int_{R}^{r} E \: dr$

• V_(0) is the potential at the surface of the shell, V is the potential inside the shell.

• Now, we know that value of E inside the shell will be zero.

$\displaystyle \implies \: \int_{V_{0}}^{V} dV = \int_{R}^{r} 0\: dr$

$\displaystyle \implies \: \int_{V_{0}}^{V} dV = 0$

$\displaystyle \implies \: V - V_{0} = 0$

$\displaystyle \implies \: V = V_{0}$

This means that gravitational potential inside the shell will be equal that on the surface of the shell.

$\boxed{ \bold{ \implies \: V = V_{0} = \dfrac{GM}{R} }}$

• G is Universal Gravitational Constant, M mass of the shell, R is radius of shell.

Hope It Helps.