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7. gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics7. gravitation1 Mark
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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