JEE Main 2025 — Gravitation Question with Solution

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, $$F_C=F_4$$

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

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

Angular momentum of the planet, $$L=mvr$$

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

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

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

M is same for both.

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

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

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