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Standard XII

Physics

COE in SHM

A uniform sol...

Question

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 :-

- \frac{2}{3} \frac{G M}{R}

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- \frac{5}{6} \frac{G M}{R}

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- \frac{4}{3} \frac{G M}{R}

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- \frac{7}{6} \frac{G M}{R}

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Solution

The correct option is D $- \frac{7}{6} \frac{G M}{R}$
$\begin{matrix} V = \frac{- G M}{(\frac{3 R}{2})} + (\frac{- G}{2 R}) = \frac{- G M}{3 R} - \frac{G M}{2 R} = \frac{- 7 G M}{6 R} H e n c e, o p t i o n D i s c o r r e c t a n s w e r . \end{matrix}$

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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 32R from the centgre is :-

The correct option is D −76GMRV=−GM(3R2)+(−G2R)=−GM3R−GM2R=−7GM6RHence,optionDiscorrectanswer.

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 :-

The correct option is D $- \frac{7}{6} \frac{G M}{R}$
$\begin{matrix} V = \frac{- G M}{(\frac{3 R}{2})} + (\frac{- G}{2 R}) = \frac{- G M}{3 R} - \frac{G M}{2 R} = \frac{- 7 G M}{6 R} H e n c e, o p t i o n D i s c o r r e c t a n s w e r . \end{matrix}$