Question
The weight of a body at depth d is equal to the weight of the body at height h above the surface of the earth. What is the ratio of h to d, for small value of h and d?
OR
Prove that the distance we have to cover into the earth below its surface is twice the distance we have to cover above the surface of the earth to get the same change in the weight of a body?
Solution
For small value of h, the acceleration due to gravity at height h is,
∴
Similarly, at the depth d the weight of body is,
Since,
i.e.,
∴
∴
Similarly, at the depth d the weight of body is,
Since,
i.e.,
∴
