Question

Taking the gravitational potential at a point infinte distance away as zero, the gravitational potential at a point $A$ is $-5$ unit. If the gravitational potential at a point infinite distance away is taken as $+10$ units, the potential at a point $A$ is

• A. $-5$ unit
• B. $+5$ unit
• C. $+10$ unit
• D. $+15$ unit

Answer 1

The correct option is B $+5$ unit

The gravitational potential $V$ at a point distance ${}^{\prime }{r}^{\prime }$ from a body a mass $m$ is equal to the amount of work done in moving a unit mass from infinity to that point
$V_r-V_{\infty }=-{\int }_{\infty }^r\overline{E}.d\overline{r}=-GM(1/r-1/\infty )$
$=\frac{-GM}{r}[As\overline{E}=\frac{-dV}{dr}]$
$\left(i\right)$ In the first case
when $V_{\infty }=0,V_r=\frac{-GM}{r}=-5$ unit
$\left(ii\right)$ In the second case $V_{\infty }=+10$ unit
$V_r-10=-5$
or $V_r=+5$ unit