Question

A spherical shell is cut into two pieces along a chord as shown in the figure. P is a point on the plane of the chord. The gravitational field at P due to the upper part is $I_1$ and that due to the lower part is $I_2$. What is the relation between them?

• A. $I_1>I_2$
• B. $I_1<I_2$
• C. $I_1=I_2$
• D. No definite relation

Answer 1

The correct option is C $I_1=I_2$

Gravitational field at P due to upper half is $\overrightarrow{I_1}$ and due to lower half is $\overrightarrow{I_2}$

Inside a hollow spherical shell since all gravitational lines are radially outwards, field is zero$\Rightarrow \overrightarrow{I_1}+\overrightarrow{I_2}=0\Rightarrow \overrightarrow{I_1}=-\overrightarrow{I_2}\Rightarrow \left|\overrightarrow{I_1}\right|=\left|\overrightarrow{I_2}\right|\Rightarrow I_1=I_2$