A planet ($\mathrm{P}_{1}$) is moving around the star of mass 2 M in the orbit of radius R. Another planet ($\mathrm{P}_{2}$) 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 ____.

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Gravitation

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✓ Correct
(C)4
(D) $\frac{1}{4}$

Answer: (B)

Solution

Kepler's third law for a body orbiting a star of mass

M_{s}

gives

T^{2} = \frac{4 π ^{2}}{G M _{s}} r^{3}

, so

T \propto r^{3} / M_{s}

. Taking the ratio for the two planets,

\frac{T _{P_{2}}}{T _{P_{1}}} = \frac{( 2 R ) ^{3} /4 M}{R ^{3} /2 M} = \frac{8}{4} \cdot \frac{2}{1} = 4 = 2

. The ratio of the periods

T_{P_{2}} : T_{P_{1}}

2

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Gravitation →

More JEE Main questions on Gravitation

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ______ m/s.
JEE Main 2026View solution →
Net gravitational force at the centre of a square is found to be $F_{1}$ when four particles having mass $M, 2 M, 3 M$ and $4 M$ are placed at the four corners of the square as shown in figure and it is $F_{2}$ when the positions of $3 M$ and $4 M$ are interchanged. The ratio …
JEE Main 2026View solution →
Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is …
JEE Main 2026View solution →
Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ______ J.
(Gravitational constant …
JEE Main 2026View solution →
Initially a satellite of 100 kg is in a circular orbit of radius $1.5 R_{E}$ . This satellite can be moved to a circular orbit of radius $3 R_{E}$ by supplying $α \times 1 0^{6} J$ of energy. The value of $α$ is ______.
(Take …
JEE Main 2026View solution →
If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ____.
(Take radius of earth to be 6400 km and $g = 9.8 m / s^{2}$ )
JEE Main 2026View solution →