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The acceleration due to gravity at depth...

The acceleration due to gravity at depth 'd' reduced by 25% from the value at the surface. Calculate the value of 'd' if radius of earth is 6,400 km.

Text Solution

Verified by Experts

We are given, Radius of earth ( R)= 6400km
Reduced value of acceleration due to gravity = 25% of g.
We are to calculate, Depth (d) at which g becomes 25% of its value.
Using relation `g_(d)= g [i-(d)/( R)]` …(i)
As `g_(d)= 25%` of `g= (g)/(4)`
So equation (i) becomes
`(g)/(4) = g[1- (d)/(6400)] rArr (1)/(4)=1 - (d)/(6400)`
`(d)/(6400)= (3)/(4) rArr d= 4800 km`
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