JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Gravitation

The minimum and maximum distances of a planet revolving around the Sun are

x_{1}

and

x_{2}

. If the minimum speed of the planet on its trajectory is

v_{0}

then its maximum speed will be :

Answer: (C)

Solution

The gravitational pull is always directed at the Sun, so the torque about the Sun vanishes and the angular momentum

m v r

stays constant. Speed and distance therefore vary oppositely: the planet is slowest at the farthest point

x_{2}

and fastest at the nearest point

x_{1}

. Equating the angular momentum at the two ends of the major axis,

m v_{m a x} x_{1} = m v_{0} x_{2}

v_{m a x} = \frac{v _{0} x _{2}}{x _{1}}

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Single correct option