Question
Physics Question on Gravitation
If the radius of earth of R then the height h at which the value of g becomes one-fourth, will be
A
8R
B
83R
C
43R
D
2R
Answer
83R
Explanation
Solution
The value of acceleration due to gravity at a height h above the surface of the earth is given by
g′=(1+Rh)2g
where R is radius of earth. When li is negligible compared to R, we have
g′=g(1+Rh)−2=g(1−R2h)
Given g′=4g
4g=g(1−R2h)
⇒41=1−R2h
⇒R2h=43
⇒h=83RNote : The value of acceleration due to gravity decreases on going above or below the surface of earth.