Gravitation Question 1

Question: If the change in the value of ?g? at a height h above the surface of the earth is the same as at a depth x below it, then (both x and h being much smaller than the radius of the earth)[NCERT 1983; BHU 2002]

Options:

A) $ [x=h] $

B) $ [x=2h] $

C) $ [x=\frac{h}{2}] $

D) $ [x=h^{2}] $

Show Answer

Answer:

Correct Answer: B

Solution:

The value of g at the height h from the surface of earth $ [{g}’=g,\left( 1-\frac{2h}{R} \right)] $

The value of g at depth x below the surface of earth $ [{g}’=g,\left( 1-\frac{x}{R} \right)] $

These two are given equal, hence $ [\left( 1-\frac{2h}{R} \right)=\left( 1-\frac{x}{R} \right)] $

On solving, we get $ [x=2h] $



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