You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Physics

Universal Law of Gravitation

A planet is m...

Question

A planet is moving along an elliptical orbit is closest to the sun at a distance $r_{1}$ and farthest away at a distance $r_{2}$ . If $v_{1}$ and $v_{2}$ are the linear velocities at the points respectively, then the ratio $v_{1} / v_{2}$ is

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r_{1} / r_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r_{2} / r_{1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $r_{2} / r_{1}$
By Kepler's third law, we know that.
$\frac{d A}{d t} = \frac{L}{2 m}$
The angular momentum is a constant.
$L_{A} = L_{B}$
$m v_{1} r_{1} = m v_{2} r_{2}$
$v_{1} r_{1} = v_{2} r_{2}$
$\frac{v_{1}}{v_{2}} = \frac{r_{2}}{r_{1}}$

Suggest Corrections

Similar questions

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}}

Q. Two particles 'A' and 'B', move with constant velocities

_{1}

and

_{2}

respectively. At the initial moment, their position vectors are

_{1}

and

_{2}

respectively. The condition for particle 'A' and 'B' for their collision is

A planet P is moving in an elliptical path around the sun S. Speed of planet in positions P and Q are $v_{1}$ and $v_{2}$ respectively with SP= $r_{1}$ and SQ= $r_{2}$ , then $\frac{v_{1}}{v_{2}}$ is equal to

Q. Two planets are revolving around the Earth with velocities

v_{1}, v_{2}

and in radii

r_{1}

and

r_{2}

(

r_{1} > r_{2}

) respectively. Then

Q. The emf (V) and internal resistance (

r

) of a single battery which is equivalent to a parallel combination of two batteries of emf's

V_{1}

and

V_{2}

and internal resistance

r_{1}

and

r_{2}

, respectively, with polarities as shown in the figure are given by

\frac{V_{1} r_{2} - V_{2} r_{1}}{r_{1} + r_{2}}, \frac{r_{1} r_{2}}{r_{1} + r_{2}}

Join BYJU'S Learning Program

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

The correct option is D r2/r1By Kepler's third law, we know that.dAdt=L2mThe angular momentum is a constant.LA=LBmv1r1=mv2r2v1r1=v2r2v1v2=r2r1

A planet is moving along an elliptical orbit is closest to the sun at a distance $r_{1}$ and farthest away at a distance $r_{2}$ . If $v_{1}$ and $v_{2}$ are the linear velocities at the points respectively, then the ratio $v_{1} / v_{2}$ is

The correct option is D $r_{2} / r_{1}$
By Kepler's third law, we know that.
$\frac{d A}{d t} = \frac{L}{2 m}$
The angular momentum is a constant.
$L_{A} = L_{B}$
$m v_{1} r_{1} = m v_{2} r_{2}$
$v_{1} r_{1} = v_{2} r_{2}$
$\frac{v_{1}}{v_{2}} = \frac{r_{2}}{r_{1}}$