Gravitation - Result Question 16

16. The height at which the weight of a body becomes $1 / 16$ th, its weight on the surface of earth (radius $R$ ), is :

[2012]

(a) $5 R$

(b) $15 R$

(c) $3 R$

(d) $4 R$

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Answer:

Correct Answer: 16. (c)

Solution:

(c) $\frac{G M_m}{(R+h)^{2}}=\frac{1 G M_m}{16 R^{2}}$

$\Rightarrow \frac{1}{(R+h)^{2}}=\frac{1}{16 R^{2}}$

$\Rightarrow \frac{R}{(R+h)}=\frac{1}{4}$

$\Rightarrow \quad \frac{R+h}{R}=4$

$\Rightarrow h=3 R$



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