Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth?

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Solution

Q.
Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth [2024]

1 300 N

2 75 N

3 225 N

4 375 N

Ans.
(3)

At surface: $m g_{s} = 300 N \Rightarrow m = \frac{300}{g_{s}}$

Gravitational field at $\frac{R}{4}$ depth under surface, $g_{d} = g_{s} [1 - \frac{d}{R}]$

$g_{d} = g_{s} [1 - \frac{R}{4 R}] = \frac{3 g_{s}}{4}$

Weight at depth, $W_{d} = m \times g_{d} = m \times \frac{3 g_{s}}{4} = \frac{3}{4} \times 300 = 225 N$

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