Question

If 'g' on the surface of the earth is 9.8 ms, find its value at a depth
3200 km (Radius of the earth = 6400 km)
A) 3.9 ms 2 B) 4.9 ms?
C) 5.9 ms? D) 6.9 ms?
25 If on the surface of the carth is 9.8 ms , find its value at a height​

Answer 1

Hey dear,

◆ Answer-

g' = 8.48 m/s^2

◆ Explaination-

# Given-

g = 9.8 m/s^2

R = 6400 km = 6.4×10^6 m

h = 480 km = 4.8×10^5 m

# Solution-

Gravitational acceleration at earth's surface is-

g = GM / R^2

Gravitational acceleration at height h is-

g' = GM / (R+h)^2

Dividing (2) by (1),

g'/g = R^2 / (R+h)^2

g' = gR^2 / (R+h)^2

Substituting values-

g' = 9.8×(6.4×10^6)^2 / (64×10^5+4.8×10^5)^2

g' = 9.8 × 0.8653

g' = 8.48 m/s^2

Therefore, acceleration due to gravity at height 580 km is 8.48 m/s^2.

Hop3 it helps