Gravitation Question 32

Question: Let g be the acceleration due to gravity at earth’s surface and K be the rotational kinetic energy of the earth. Suppose the earth’s radius decreases by 2% keeping all other quantities same, then [BHU 1994; JIPMER 2000]

Options:

A) g decreases by 2% and K decreases by 4%

B) g decreases by 4% and K increases by 2%

C) g increases by 4% and K increases by 4%

D) g decreases by 4% and K increases by 4%

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Answer:

Correct Answer: C

Solution:

$ [g=\frac{GM}{R^{2}}] $

and $ [K=\frac{L^{2}}{2I}] $

If mass of the earth and its angular momentum remains constant then

$ [g\propto \frac{1}{R^{2}}] $

and $ [K\propto \frac{1}{R^{2}}] $ i.e.

if radius of earth decreases by 2% then g and K both increases by 4%.



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