NEET Physics Alternating Current / प्रत्यावर्ती धारा NEET PYQ-Alternating Current

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 \[{{r}_{2}}\] are the linear velocities at these points respectively, then the ratio \[\frac{{{v}_{1}}}{{{v}_{2}}}\] is                                                                               [AIPMT (S) 2011]

A) \[{{r}_{2}}/{{r}_{1}}\]

B)      \[{{({{r}_{2}}/{{r}_{1}})}^{2}}\]

C) \[{{r}_{1}}/{{r}_{2}}\]

D)      \[{{({{r}_{1}}/{{r}_{2}})}^{2}}\]

Correct Answer: A

Solution :

From the law of conservation of angular momentum

\[m{{r}_{1}}{{v}_{1}}=m{{r}_{2}}{{v}_{2}}\]

\[{{r}_{1}}{{v}_{1}}={{r}_{2}}{{v}_{2}}\]

\[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{r}_{2}}}{{{r}_{1}}}\]