Taking the gravitational potential at a point infinte distance aw… - Vidyadip

MCQ

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 point infinite distance away is taken as $+ 10\, units$, the potential at point $A$ is ......... $unit$

A
$-5$
✓
$+ 5$
C
$+10$
D
$+15$

✓

Answer

Correct option: B.

$+ 5$

b
The gravitational potential $V$ at a point distance $'r'$ from a body of mass $m$ is equal to the amount of work done in moving a unit mass from infinity to that point.

${V_r} - {v_ \propto } = - \int\limits_ \propto ^r {\overrightarrow E .d\overrightarrow r } = - GM\left( {1/r - 1/ \propto } \right)$

$ = \frac{{ - GM}}{r}\left( {As\,\overrightarrow E = \frac{{ - dv}}{{dr}}} \right)$

$(i)$ In the first case

$when\,{v_ \propto } = 0,\,{V_r} = \frac{{ - GM}}{r} = - 5\,unit$

$(ii)$ In the second case ${v^ \propto } = + 10\,unit$

${V_r} - 10 = - 5$

or ${V_r} = + 5\,unit$

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