Question

If the gravitational potential due to the earth at infinite distance from it is zero, the potential at a point $P$ is $-5{\text{J kg}}^{-1}$. Suppose we arbitrarily assume the gravitational potential at infinity to be $+10{\text{J kg}}^{-1}$. Then, gravitational potential at $P$ will be

• A. $-5{\text{J kg}}^{-1}$
• B. $+5{\text{J kg}}^{-1}$
• C. $-15{\text{J kg}}^{-1}$
• D. $+15{\text{J kg}}^{-1}$

Answer 1

The correct option is B $+5{\text{J kg}}^{-1}$

Given that,
Potential at $P,V_P=-5{\text{J kg}}^{-1}$
The gravitational potential is a scalar quantity and change in gravitational potential doesn’t depend on the reference chosen.
For $1$st case:
$\Delta V=V_P-V_{\infty }$
$\Rightarrow \Delta V=-5{\text{J/kg}}^{-1}$
For $2$nd case:
$\Delta V=V_P-V_{\infty }$
$\Rightarrow V_P=V_{\infty }+\Delta V$
$\Rightarrow V_P=10-5$
$\Rightarrow V_P=+5{\text{J kg}}^{-1}$
Hence, option (b) is correct.

Why this question? To familiarize students with the concept of gravitational potential and that it doesn’t depend on the reference chosen.