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

Byju's Answer

Standard XII

Physics

Kepler's Law

A planet is r...

Question

A planet is revolving in an elliptical orbit around the sun. Its closest distance from the sun is $r$ and the farthest distance is $R$ . If the velocity of the planet nearest to the sun be $v$ and that farthest away from the sun be $V$ , then $v / V$ is :

R^{2} / r^{2}

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

r^{2} / R^{2}

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

R / r

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

r / R

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

Open in App

Solution

The correct option is C $R / r$
As angular momentum is conserved, hence we have the equation:

$I_{1} ω_{1} = I_{2} ω_{2}$

For elliptical body, $I = M r^{2} .$

So,

$M R_{1}^{2} ω_{1} = M R_{1}^{2} ω_{2}$

$M R_{1} v_{1} = M R_{2} v_{2}$

(Since, $ω = \frac{v}{R})$

So, $R_{1} v_{1} = R_{2} v_{2}$

i.e. $R V = v r$
$(S i n c e, v_{2} = V a n d v_{1} = v)$

$\frac{v}{V} = \frac{R}{r}$

Thus option C is correct.

Suggest Corrections

Similar questions

Q. A planet is revolving around the Sun in an elliptical orbit. Its closest distance from the Sun is

r

and farthest distance is

R

. If the orbital velocity of the planet closest to the Sun is

v

, then what is the velocity at the farthest point?

Q. A planet is revolving in an elliptical orbit around the Sun. Its closest distance from the Sun is

r_{m i n}

and the farthest distance is

r_{m a x}

. If the velocity of the planet at the distance of the closest approach is

ν_{1}

and that at the farthest distance from the Sun is

ν_{2}

, then {

ν_{1}

}/{

ν_{2}

}

Q. A planet in its elliptical orbit has the farthest distance from the sun(

r_{1}

) equal to three times its nearest distance from the sun(

r_{2}

). Will the orbital speed of the planet be different at those points?

Q. A planet of mass

m

is revolving around the sun of mass

M

in an elliptical orbit. If

r

and

R

are the minimum and maximum distances of the planet from the sun respectively,

v

and

V

are the minimum and maximum speed of the planet respectively, then

When a planet orbiting around the sun an elliptical orbit R1 and R2 are the closest and farthest distance from the sun Then the ratio of the magnitudes of maximum and minimum gravitational forces between them is

A.r1:r2

B.r2:r1

C.r1^2:r2^2

D.r2^2:r1^2

Join BYJU'S Learning Program

A planet is revolving in an elliptical orbit around the sun. Its closest distance from the sun is r and the farthest distance is R. If the velocity of the planet nearest to the sun be v and that farthest away from the sun be V, then v/V is :

The correct option is C R/rAs angular momentum is conserved, hence we have the equation: I1ω1=I2ω2 For elliptical body, I=Mr2. So, MR21ω1=MR21ω2 MR1v1=MR2v2 (Since, ω=vR) So, R1v1=R2v2 i.e. RV=vr(Since, v2=V and v1=v) vV=Rr Thus option C is correct.

A planet is revolving in an elliptical orbit around the sun. Its closest distance from the sun is $r$ and the farthest distance is $R$ . If the velocity of the planet nearest to the sun be $v$ and that farthest away from the sun be $V$ , then $v / V$ is :