Question

A spherical shell is cut into two pieces along a chord and separated by a large distance as shown in figure. For points $A$ and $B$, where $V$ and $\overrightarrow{E}$ are gravitational potential and field respectively, then

• A. $V_A=V_B\text{and}|{\overrightarrow{E}}_A|>|{\overrightarrow{E}}_B|$
• B. $V_A<V_B\text{and}|{\overrightarrow{E}}_A|=|{\overrightarrow{E}}_B|$
• C. $V_A=V_B\text{and}|{\overrightarrow{E}}_A|=|{\overrightarrow{E}}_B|$
• D. $V_A>V_B\text{and}|{\overrightarrow{E}}_A|<|{\overrightarrow{E}}_B|$

Answer 1

The correct option is B $V_A<V_B\text{and}|{\overrightarrow{E}}_A|=|{\overrightarrow{E}}_B|$

Since the net gravitational field inside a spherical shell is zero
${\overrightarrow{E}}_A+{\overrightarrow{E}}_B=0$
$|{\overrightarrow{E}}_A|=|{\overrightarrow{E}}_B|$
Analyzing gravitational field lines, $V_A<V_B$