A planet moving along an elliptical orbit is closest to the sun at a distance r1 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 ( v 1/ v 2) is:

Question

A planet moving along an elliptical orbit is closest to the sun at a distance r1 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 ( v 1/ v 2) is: (A)  ( r1 / r2)2  (B) ( r2 / r1)  (C) ( r2 / r1) 2  (D) ( r1 / r2)

Tardigrade Admin · Accepted Answer

According to the law of conservation of angular momentum L1 =L2 m v1 r1 =m v2 r2 ⇒ v1 r1=v2 r2 or (v1/v2)=(r2/r1)

Q. 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:

$(r_{1} / r_{2})^{2}$

$(r_{2} / r_{1})$

$(r_{2} / r_{1})^{2}$

$(r_{1} / r_{2})$

According to the law of conservation of angular momentum
$L_{1} = L_{2}$
$m v_{1} r_{1} = m v_{2} r_{2}$
$\Rightarrow v_{1} r_{1} = v_{2} r_{2}$
or $\frac{v _{1}}{v _{2}} = \frac{r _{2}}{r _{1}}$

Q. A planet moving along an elliptical orbit is closest to the sun at a distance r1​ and farthest away at a distance of r2​. If v1​ and v2​ are the linear velocities at these points respectively, then the ratio v2​v1​​ is:

(r1​/r2​)2

(r2​/r1​)

(r2​/r1​)2

(r1​/r2​)