A metal sphere has radius R and mass m. A spherical hollow of diameter R is made in this sphere such that its surface passes through the centre of the metal sphere and touches the outside surface of the metal sphere. A unit mass is placed at a distance from the centre of the metal sphere. The gravitational field at that point is (a) ((GM)/R^2 ) (1−(1/(8(1−((2R)/a))^2 ))) (b) ((GM)/a^2 ) (1−(1/(8(1−(R/(2a)))^2 ))) (c) ((GM)/((R+a)^2 )) (1−(1/(8(1−(R/(2a)))^2 ))) (d) ((GM)/((R−a)^2 )) (1−(1/(8(1−((2a)/R))^2 )))


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Question Number 173558 by MadhumitaSamanta last updated on 13/Jul/22

$A metal sphere has radius R and mass m . A spherical$ $hollow of diameter R is made in this sphere such that its$ $surface passes through the centre of the metal sphere$ $and touches the outside surface of the metal sphere .$ $A unit mass is placed at a distance from the centre of the metal$ $sphere . The gravitational field at that point is$ $(a) \frac{G M}{R^{2}} (1 - \frac{1}{8 {(1 - \frac{2 R}{a})}^{2}})$ $(b) \frac{G M}{a^{2}} (1 - \frac{1}{8 {(1 - \frac{R}{2 a})}^{2}})$ $(c) \frac{G M}{{(R + a)}^{2}} (1 - \frac{1}{8 {(1 - \frac{R}{2 a})}^{2}})$ $(d) \frac{G M}{{(R - a)}^{2}} (1 - \frac{1}{8 {(1 - \frac{2 a}{R})}^{2}})$
Commented by MadhumitaSamanta last updated on 13/Jul/22

	Answered by aleks041103 last updated on 13/Jul/22

	$W e c a n s a y t h a t t h e m e t a l e l e m e n t i s$ $a s u p e r p o s i t i o n o f a s p h e r e o f r a d i u s R$ $a n d m a s s m a n d a s p h e r e o f d i a m e t e r R$ $a n d m a s s - \frac{m}{8}$ $\Rightarrow F = \frac{G m}{a^{2}} + \frac{G (- \frac{m}{8})}{{(a - R / 2)}^{2}} = \frac{G m}{a^{2}} (1 - \frac{1}{8 {(1 - \frac{R}{2 a})}^{2}})$ $\Rightarrow A n s . (b)$
	Commented by Tawa11 last updated on 13/Jul/22

	$Great sir$
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