A spherical hole is made in a solid sphere of radius R. The mass of the sphere before hollowing was M. The gravitational field at the centre of the hole due to the remaining mass is

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$\frac{GM}{2 R^{2}}$

$\frac{GM}{8 R^{2}}$

Zero

answer is D.

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Detailed Solution

E due to complete sphere at center of hole = $\frac{GM \frac{R}{2}}{R^{3}} = \frac{GM}{2 R^{2}}$
E due to hole at it's centre = 0
$∴$ E due to remaining part of Sphere $= \frac{GM}{2 R^{2}}$

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