A comet revolves around the sun in an elliptical orbit. When it is closest to the sun at distance d , then its corresponding kinetic energy is k0. If it is farthest from the sun at distance 3d then the corresponding kinetic energy will be

Question

A comet revolves around the sun in an elliptical orbit. When it is closest to the sun at distance d , then its corresponding kinetic energy is k0. If it is farthest from the sun at distance 3d then the corresponding kinetic energy will be (A) (k0/9) (B) (8k0/9) (C) (k0/4) (D) (4k0/9)

Tardigrade Admin · Accepted Answer

v1r1=v2r2= constant ∴ v0d=3dv1 ⇒ v1=(v0/3) ∴ KE=(1/2)(mv02/9) ⇒ KE=(k0/9)

Q. A comet revolves around the sun in an elliptical orbit. When it is closest to the sun at distance $d$ , then its corresponding kinetic energy is $k_{0} .$ If it is farthest from the sun at distance $3 d$ then the corresponding kinetic energy will be

$\frac{k _{0}}{9}$

$\frac{8 k _{0}}{9}$

$\frac{k _{0}}{4}$

$\frac{4 k _{0}}{9}$

$v_{1} r_{1} = v_{2} r_{2} =$ constant
$∴ v_{0} d = 3 d v_{1}$
$\Rightarrow v_{1} = \frac{v _{0}}{3}$
$∴ K E = \frac{1}{2} \frac{m v _{0}^{2}}{9}$
$\Rightarrow K E = \frac{k _{0}}{9}$

Q. A comet revolves around the sun in an elliptical orbit. When it is closest to the sun at distance d , then its corresponding kinetic energy is k0​. If it is farthest from the sun at distance 3d then the corresponding kinetic energy will be

9k0​​

98k0​​

4k0​​

94k0​​