JEE PYQ: Gravitation Question 20
Question 20 - 2020 (02 Sep Shift 2)
The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is $R$ and effect of the rotation of the earth is neglected):
(1) $\frac{\sqrt{5}R - R}{2}$
(2) $\frac{R}{2}$
(3) $\frac{\sqrt{5R}-R}{2}$
(4) $\frac{\sqrt{3R}-R}{2}$
Show Answer
Answer: (3)
Solution
$\frac{GM}{(R+h)^2} = \frac{GM}{R^3}(R-h)$. $R^3 = (R+h)^2(R-h)$. Expanding and simplifying: $h^2 + hR - R^2 = 0$. $h = \frac{-R + \sqrt{R^2 + 4R^2}}{2} = \frac{(\sqrt{5}-1)R}{2}$.
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