Question:
The escape velocity for the earth is $11.2 \,km / sec$. The mass of another planet $100$ times mass of earth and its radius is $4$ times radius of the earth. The escape velocity for the planet is:
The escape velocity for the earth is $11.2 \,km / sec$. The mass of another planet $100$ times mass of earth and its radius is $4$ times radius of the earth. The escape velocity for the planet is:
Updated On: Aug 15, 2022
- 56.0 km/sec
- 280 km/sec
- 112 km/sec
- 56 km/sec
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The Correct Option is A
Solution and Explanation
$v_{\text {escape }}=\sqrt{\frac{2 G M}{R}} \propto \sqrt{\frac{M}{R}}$,
Hence, $\frac{v_{p}}{v_{e}}=\sqrt{\frac{M_{p}}{R_{p}} \times \frac{R_{e}}{M_{e}}}$
or $\frac{v_{p}}{v_{e}}=\sqrt{100 \times \frac{1}{4}}=5$
$v_{p}=5 \times 11.2=56 \,km / sec$
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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].