JEE Main 2026 — Apr 2, Shift 1 — Physics solution

JEE Main2026Apr 2, Shift 1Physics

A planet $(P_{1})$ is moving around the star of mass $2 M$ in the orbit of radius $R$ . Another planet $(P_{2})$ is moving around another star of mass $4 M$ in a orbit of radius $2 R$ . Ratio of time periods of revolution of $P_{2}$ and $P_{1}$ is ___________.

A
$\frac{1}{2}$
B
$2$
C
$4$
D
$\frac{1}{4}$

Solution

From Kepler's third law, $T = \frac{2 π}{G M _{star}} r^{3/2}$ .

Therefore the ratio is:

$\frac{T _{P_{2}}}{T _{P_{1}}} = \frac{M _{1}}{M _{2}} \cdot (\frac{r _{2}}{r _{1}})^{3/2} = \frac{2 M}{4 M} \cdot (\frac{2 R}{R})^{3/2}$

$= \frac{1}{2} \cdot 22 = 2$

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