Question:
A body weighs $200\,N$ on the surface of the earth How much will it weigh half way down to the centre of the earth ?
A body weighs $200\,N$ on the surface of the earth How much will it weigh half way down to the centre of the earth ?
Updated On: Mar 14, 2024
- 250 N
- 100 N
- 150 N
- 200 N
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The Correct Option is B
Solution and Explanation
Acceleration due to gravity at a depth d from surface of earth
$g' =g\left(1- \frac{d}{R}\right) $ ...(1)
Where g = acceleration due to gravity at earth's surface
Multiplying by mass 'm' on both sides of (1)
$mg' =mg\left(1- \frac{d}{R}\right) \left(d = \frac{R}{2}\right)$
$ = 200\left(1-\frac{R}{2R}\right) = \frac{200}{2} = 100 N$
$g' =g\left(1- \frac{d}{R}\right) $ ...(1)
Where g = acceleration due to gravity at earth's surface
Multiplying by mass 'm' on both sides of (1)
$mg' =mg\left(1- \frac{d}{R}\right) \left(d = \frac{R}{2}\right)$
$ = 200\left(1-\frac{R}{2R}\right) = \frac{200}{2} = 100 N$
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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].