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>>Physics
>>Gravitation
>>Variation in Value of Acceleration due to Gravity
>> $The height at which the weight of a body$

Question

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

A

4R

B

5R

C

15R

D

3R

Medium

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Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is D)

$\frac{G M m}{( R + h ) ^{2}} = \frac{1}{1 6} \frac{G M m}{R ^{2}} \frac{1}{( R + h ) ^{2}} = \frac{1}{1 6 R ^{2}} o r, (\frac{R}{R + h})^{2} = \frac{1}{1 6} \Rightarrow \frac{R}{R + h} = \frac{1}{4} . ∴ R + h = 4 R \Rightarrow h = 3 R$

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