Question

On the surface of earth acceleration due to gravity is g and gravitational potential is V match the following:

Table - 1	Table -2
(A) At height h = R value of g	(P) decrease by a factor (1/4)
(B) At depth h = (R/2)	(Q) decrease by a factor (1/2)
(C) At height h = R value of v	(R) increase by a factor (11 / 8)
(D) At depth h = (R/2) value of v	(S) increase by a factor 2
	(T) None

Answer 1

A -P,  

B-Q,  

C-S,  

D-T

On the earth surface acceleration = g & potential is V

(A) g' = [g / {1 + (h/R)}²] --------- acceleration at height h.

at h = R

g' = [g / {1 + (R/R)}²] = (g/4)

i.e. decrease by factor (1/4)

(B) at depth d, g' = g[1 – (d/R)]

here   d = (R/2)

∴   g' = g[1 – {(R/2) × (1/R)}] = (g/2)

i.e.   decreases by factor (1/2)

(C) gravitational potential ∝ distance       i.e.      V ∝ (R + h)

 ∴ at height h = R, V becomes twice of original value.

(D) None option.