Question:
If density of earth increases $4$ times and its radius becomes half of what it is, our weight will
If density of earth increases $4$ times and its radius becomes half of what it is, our weight will
Updated On: Aug 15, 2022
- be 4 times its present value
- be doubled
- remain same
- be halved
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The Correct Option is B
Solution and Explanation
Weight, $w = mg = m \frac{4}{3} \pi GR \rho$
Now that: $R'=R / 2$ and $\rho'=4 \rho$
$\therefore \frac{w'}{w}=\frac{R' \rho'}{R \rho}=\left(\frac{1}{2}\right) \times 4=2$
$w'=2 w$
Hence our weight will be doubled.
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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].