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The depth at which the effective value of acceleration due to gravity is g/4

The depth at which the effective value of acceleration due to gravity is g/4 is (R=Radius of earth)

Options

(a) R
(b) 3R/4
(c) R/2
(d) R/4

Correct Answer:

3R/4

Explanation:

The effect of depth of acceleration due to gravity is g’=g(1-d/R)
Given, g’=g/4
g/4=g(1-d/R)
(g/4)/g=(1-d/R)
1/4=1-d/R ⇒d/R=1-1/4 ⇒3/4
d=3R/4

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