Question:
A planet moving along an elliptical orbit is closest to the sun at a distance $r_{1}$ and farthest away at a distance of $r _{2}$. If $v _{1}$ and $v _{2}$ are the linear velocities at these points respectively,
then the ratio $\frac{ v _{1}}{ v _{2}}$ is:
A planet moving along an elliptical orbit is closest to the sun at a distance $r_{1}$ and farthest away at a distance of $r _{2}$. If $v _{1}$ and $v _{2}$ are the linear velocities at these points respectively,
then the ratio $\frac{ v _{1}}{ v _{2}}$ is:
Updated On: May 25, 2022
- $ ( r_1 / r_2)^2 $
- $( r_2 / r_1) $
- $( r_2 / r_1) ^2 $
- $( r_1 / r_2)$
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The Correct Option is B
Solution and Explanation
$V_{1} r _{1}= V _{2} r _{2}$
$\frac{ V _{1}}{ V _{2}}=\frac{ r _{2}}{ r _{1}}$
$\frac{ V _{1}}{ V _{2}}=\frac{ r _{2}}{ r _{1}}$
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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].