Question

Calculate the ratio of weights of a body when it is (radius of the Earth is 6400km.)

1. 200 km above the surface of the Earth and

2. 200 km below the surface of the Earth.

• A. 0.97
• B. 1.2
• C. 2
• D. 0

Answer 1

The correct option is A 0.97

The acceleration Due to Gravity variation on :-

at an height 'h' $g_1^1=g(\frac{R}{R+h}{)}^2$ at adept 'd'$g_2^1=g(1-\frac{d}{R})$

where g : at surface and R : Radius of Earth

an weight of body, w = mg', mg',$g^{\prime }$ accln. due to gravity at that point.

Ratio of weights :-

$\frac{w_1}{w_2}=(\frac{R}{R+h}{)}^2\times (\frac{R}{R-d})$

From question, R = 6400km, d = h = 200km so,

$\frac{w_1}{w_2}=\frac{(64000{)}^3}{(6400+200{)}^2(6400-200)}=\frac{(6400{)}^3}{\left(6600{)}^2\right(6200)}\simeq 0.97$ (Ans)