Gravitation - Result Question 43
46. 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
[2011]
(a) $(r_1 / r_2)^{2}$
(b) $r_2 / r_1$
(c) $(r_2 / r_1)^{2}$
(d) $r_1 / r_2$
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Answer:
Correct Answer: 46. (b)
Solution:
- (b) Angular momentum is conserved
$\therefore L_1=L_2$
$\Rightarrow mr_1 v_1=mr_2 v_2$
$\Rightarrow r_1 v_1=r_2 v_2$
$\Rightarrow \frac{v_1}{v_2}=\frac{r_2}{r_1}$
