Question:
Weight of body at earth's surface is W. At a depth half way to the centre of earth it will be
Weight of body at earth's surface is W. At a depth half way to the centre of earth it will be
Updated On: Jul 7, 2022
- W/8
- W/4
- W/2
- W
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The Correct Option is C
Solution and Explanation
Using $g_d = g \left( 1 - \frac{d}{R}\right)$ , we get $g_d = g \left( 1 - \frac{R}{2R} \right) = \frac{g}{2}$
$(\therefore d = \frac{R}{2} given )$
Thus weight = $mg_d = \frac{mg}{2} = \frac{W}{2}$
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].