The elongation of a wire on the surface of the earth is 10–4m. The same wire of same dimensions is elongated by 6 × 10–5m on another planet. The acceleration due to gravity on the planet will be ___ ms–2. (Take acceleration due to gravity on the surface of earth = 10 ms–2)
Correct Answer: 6
Solution and Explanation
\(\Delta I = \frac{M'gI}{2A y}\)
\(⇒\)\( Δl ∝ g\)
\(⇒\)\(\frac{g_p}{g_e} = \frac{\Delta I_p}{\Delta I_e} = \frac{6 \times 10^{-5}}{10 \times 10^{-5}}\)
\(⇒\) \(g_p = 6 m/s^2 as g_e = 10 m/s^2\)
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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].