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] $
