QJEEM25Ph4857: JEE Main 2025 Physics - Class 11 JEEM25Ph4857 Solution: Two planets, and are orbiting a common star in circular orbits…

Let a planet of mass m orbits a star of mass M in circular orbit of radius r with speed v.

For this circular motion, centripetal force is provided by the gravitational force between both masses.

Hence, ${F_C} = {F_4}$

$\Rightarrow {{m{v^2}} \over r} = {{GMm} \over {{r^2}}}$

$\Rightarrow v = \sqrt {{{Gm} \over r}}$

Angular momentum of the planet, $L = mvr$

$\Rightarrow L = m\sqrt {{{Gm} \over r}} r$

$\Rightarrow L = \sqrt {GM} m\sqrt r$

Given, ${m_B} = 4\sqrt 2 {m_A}$ and ${R_B} = 2{R_A}$

M is same for both.

So, ${{{L_B}} \over {{L_A}}} = \left( {{{{m_B}} \over {{m_A}}}} \right)\sqrt {{{{R_B}} \over {{R_A}}}}$

$= \left( {4\sqrt 2 } \right)\sqrt 2 = 4 \times 2$

$\Rightarrow {{{L_B}} \over {{L_A}}} = 8$ .