Question

If potential at the surface of earth is assigned zero value, then potential at centre of earth will be $($ Mass $=M$, Radius $=R)$

• A. 0
• B. $-\frac{G M}{2 R}$
• C. $-\frac{3 G M}{2 R}$
• D. $\frac{3 G M}{2 R}$

Answer 1

Answer: (B)

The concept involved here is that,
Gravitational potential difference between any two points in a gravitational field is independent of the choice of reference. When potential at the infinity is assigned zero value,
Potential at the surface $=-\frac{G M}{R}=V_{s}$
Potential at the centre $=-\frac{3 G M}{2 R}=V_{c}$
$V_{s}-V_{c}=-\frac{G M}{R}+\frac{3 G M}{2 R}=\frac{G M}{2 R}$
Now, when potential at the surface is assigned zero value,
$V_{s}-V_{c}=V_{s}^{\prime}-V_{c}^{\prime} $
$\Rightarrow \frac{G M}{2 R}=0-V_{c}^{\prime}$
$ \Rightarrow V_{c}^{\prime}=-\frac{G M}{2 R}$
Here, $V_{s}^{\prime}$ and $V_{c}^{\prime}$ are the new values of potential at the sum and centre respectively.