Question:
If the distance between the earth and the sun were half its present value, the number of days in a year would have been
If the distance between the earth and the sun were half its present value, the number of days in a year would have been
Updated On: Jun 14, 2022
- 64.5
- 129
- 182.5
- 730
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The Correct Option is B
Solution and Explanation
From Kepler's third law $T^2 \propto r^3 \, \, \, or \, \, \, \, T \propto (r)^{3/2}$
$\therefore \, \, \frac{T_2}{T_1} = \bigg( \frac{ r_2}{r_1}\bigg)^{3/2} \, \, \, \, or \, \, \, \, T_2 =T_1 \bigg( \frac{r_2}{r_1} \bigg)^{3/2} \, \, = (365) \bigg(\frac{1}{2} \bigg)^{3/2}$
$ \Rightarrow \, \, \, \, \, T_2 = 129 days $
$\therefore \, \, \frac{T_2}{T_1} = \bigg( \frac{ r_2}{r_1}\bigg)^{3/2} \, \, \, \, or \, \, \, \, T_2 =T_1 \bigg( \frac{r_2}{r_1} \bigg)^{3/2} \, \, = (365) \bigg(\frac{1}{2} \bigg)^{3/2}$
$ \Rightarrow \, \, \, \, \, T_2 = 129 days $
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Concepts Used:
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- (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].