Question:
The acceleration due to gravity at a height $1\, km$ above the earth is the same as at a depth $d$ below the surface of earth. Then :
The acceleration due to gravity at a height $1\, km$ above the earth is the same as at a depth $d$ below the surface of earth. Then :
Updated On: Apr 28, 2025
- $d = 1 km $
- $d = \frac{3}{2} km $
- $d = 2 k m $
- $ d = \frac{1}{2} km$
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The Correct Option is C
Solution and Explanation
Above earth surface
$g'=g\left(1-\frac{2 h}{R_{e}}\right)$
$\Delta g'=g \frac{2 h}{R_{e}}$...(1)
From (1) & (2)
$d=2 h$
$d=2 \times 1\, km$
Below earth surface
$g'=g\left(1-\frac{d}{R_{e}}\right)$
$\Delta g=g \frac{d}{R_{e}}$...(2)
$g'=g\left(1-\frac{2 h}{R_{e}}\right)$
$\Delta g'=g \frac{2 h}{R_{e}}$...(1)
From (1) & (2)
$d=2 h$
$d=2 \times 1\, km$
Below earth surface
$g'=g\left(1-\frac{d}{R_{e}}\right)$
$\Delta g=g \frac{d}{R_{e}}$...(2)
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Concepts Used:
Escape Speed
Escape speed is the minimum speed, which is required by the object to escape from the gravitational influence of a plannet. Escape speed for Earth’s surface is 11,186 m/sec.
The formula for escape speed is given below:
ve = (2GM / r)1/2
where ,
ve = Escape Velocity
G = Universal Gravitational Constant
M = Mass of the body to be escaped from
r = Distance from the centre of the mass