Gravitational potential energy of a solid hemispherical object of mass M and radius R will be

\frac{- 6 G M^{2}}{5 R}

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\frac{- 3 G M}{R}

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< \frac{- 6 G M^{2}}{5 R}

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> \frac{- 6 G M^{2}}{5 R}

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Solution

The correct option is A $\frac{- 3 G M}{R}$
Consider a hemisphere shell radius $r$ and thickness $d r$
Its mass $d m = \frac{μ}{2 / 3 π R^{3}} (2 p i r^{2} d r) \Rightarrow d m = \frac{3 M r^{2} d r}{R^{3}} d v = - \frac{- G d m}{r} = - \frac{- 3 G M r d r}{R^{3}} ∴ V = \int_{0}^{R} d v = - \frac{3 G M}{2 R}$

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Gravitational potential energy of a solid hemispherical object of mass M and radius R will be

The correct option is A −3GMRConsider a hemisphere shell radius r and thickness drIts mass dm=μ2/3πR3(2pir2dr)⇒dm=3Mr2drR3dv=−−Gdmr=−−3GMrdrR3∴V=∫R0dv=−3GM2R