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7. gravitation — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics7. gravitation1 Mark
MCQ
A uniform solid sphere of mass $M$ and radius $R$ is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius $2R$. The value of gravitational potential at a distance $\frac{3}{2}\,R$ from the centgre is 
  • A
    $ - \frac{2}{3}\,\frac{{GM}}{R}$
  • B
    $ - \frac{5}{6}\,\frac{{GM}}{R}$
  • C
    $ - \frac{4}{3}\,\frac{{GM}}{R}$
  • ✓
    $ - \frac{7}{6}\,\frac{{GM}}{R}$
✓

Answer

Correct option: D.
$ - \frac{7}{6}\,\frac{{GM}}{R}$
d
Due to solid sphere.

Gravitational potential.

$\mathrm{V}_{1}=-\frac{\mathrm{GM}}{(3 \mathrm{R} / 2)}=-\frac{2 \mathrm{GM}}{3 \mathrm{R}}$

Due to spherical shell.

Gravitational potential, $\mathrm{V}_{2}=-\frac{\mathrm{GM}}{2 \mathrm{R}}$

Net Gravitational potential

$=-\frac{2 \mathrm{GM}}{3 \mathrm{R}}-\frac{\mathrm{GM}}{2 \mathrm{R}}=-\frac{7 \mathrm{GM}}{6 \mathrm{R}}$

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