Question:
The value of g at a particular point is $9.8 \, ms^{-2}$. Suppose theearth suddenlyshrinks uniformly to half its present size without losing any mass. The value ofg at the same point (distance of the point from the centre of earth does not change) will now be
The value of g at a particular point is $9.8 \, ms^{-2}$. Suppose theearth suddenlyshrinks uniformly to half its present size without losing any mass. The value ofg at the same point (distance of the point from the centre of earth does not change) will now be
Updated On: Aug 15, 2022
- $9.8 \, ms^{-2}$
- $4.9 \, ms^{-2}$
- $19.6 \, ms^{-2}$
- $39.2 \, ms^{-2}$
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The Correct Option is A
Solution and Explanation
If $g_i$ be the initial value tor acceleration aue to gravity and $g_f$, be the final value then
$g_{i}=\frac{G M}{R^{2}}=g$ and
$g_{f}=\frac{G M}{\left(\frac{R}{2}+\frac{R}{2}\right)^{2}}=g$
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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].