The depth `d`, at which the value of acceleration due to gravity becomes 1/n times the value at the surface is (R = radius of the earth)

Options

A. `R/n`
B. `(R )/(n^2)`
C. `(R ( n - 1))/(n)`
D. `(Rn)/((n-1))`

Answer

C

Explanation

The acceleration due to gravity at a depth d from the surface of the earth is given by
` g_d = g (1- d/R) " given " , g_d = g/n`
` therefore g/n = g (1 - d/R) " or " d/R = 1 - 1/n = (n-1)/(n) " or " d = (R ( n-1))/(n)`