If `g` is the acceleration due to gravity and `R` is the radius of earth, then the dimensional formula for g `R` is

Options

A. a height `R/2` from the earth's surface
B. the centre of the earth
C. the surface of the earth
D. a depth `R/2` from earth's surface

Answer

C

Explanation

Acceleration due to gravity at a height h above the earth.s surface is ` g_h = (g)/((1 + h/R)^2)`
where g is the acceleration due to gravity on the earth.s surface.
At `h = R/2 , g_h = (g)/((1 + (R)/(2R) )^2) =(4g)/(9)`
Acceleration due to gravity at a depth d below the earth.s surface is `g_d = g (1 - d/R)`
At ` d =R/2 , g_d = g (1 -(R )/(2R) ) = g/2`
At the centre of earth, `d = R , g_d = g (1 - R/R) =0`
Thus, the acceleration due to gravity is maximum on the earth.s surface.