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In older times, people used to think that the Earth was flat. Imagine that the Earth is indeed not a sphere of radius R, but an infinite plate of thickness H. What value of H is needed to allow the same gravitational acceleration to be experienced as on the surface of the actual Earth ? (Assume that the Earth’s density is uniform and equal in the two models.)

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$\frac{2 R}{3}$

$\frac{4 R}{3}$

$\frac{8 R}{3}$

$\frac{R}{3}$

answer is A.

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Detailed Solution

Gauss law for gravitation
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$\int \vec{g} . d \vec{s} = - m_{i n} .4 π G$
$g = \frac{G M}{R^{2}}$
$2 \times \frac{G M}{R^{2}} \times A = \frac{M}{\frac{4}{3} π R^{3}} (h \times A) \times 4 π G$
$\Rightarrow h = \frac{2 R}{3}$

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