Weight of a body of mass m decreases by $1%$ when it is raised to height $h$ above the earth's surface. If the body is taken to a depth $h$ in a mine, change in its weight is
- 0.5% increase
- 1% increase
- 0.5% decrease
- 2% decrease
The Correct Option is C
Solution and Explanation
$g_d = g \left( 1 - \frac{d}{R}\right)$
where d = h (given)
Clearly d = h brings 0.5% decrease in g.
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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].