[NEET - 2020]
(a) 48 N (b) 32 N (c) 30 N 4) 24 N
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Gravitational acceleration at
height ‘h’ is
\[g_{h}=g\left ( 1+\frac{h}{R} \right )^{-2}\]
Multiplying both side by 'm' we get,
\[mg_{h}=mg\left ( 1+\frac{h}{R} \right )^{-2}\]
\[W_{h}=W\left ( 1+\frac{h}{R} \right )^{-2}\]
As, h=R/2,
\[W_{h}=W\left ( 1+\frac{\frac{R}{2}}{R} \right )^{-2}\]
\[W_{h}=W\left ( 1+\frac{1}{2} \right )^{-2}\]
\[W_{h}=W\left ( \frac{3}{2} \right )^{-2}\]
\[W_{h}=W\left ( \frac{2}{3} \right )^{2}\]
\[W_{h}=72*\left ( \frac{4}{9} \right )\]
Therefore, The gravitational force on body at a height equal to half the radius of earth is
\[W_{h}=32 N\]
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