Four particles each of mass M, move along a circle of radius R under… | JEE Main 2021 (1 Sep, Shift 2)

Q55JEE Main 2021 · 1 SEP · SHIFT 2Difficult

Satellites - Orbital Velocity & Period

Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is:

Show answer and solution

Answer: (b)

Adjacent masses: distance $\sqrt{2}R$ ; opposite mass: distance $2R$ .
Two adjacent pulls $F_1 = \frac{GM^2}{2R^2}$ at $45^\circ$ to the radius, plus $F_2 = \frac{GM^2}{4R^2}$ along it.
Net: $F = 2F_1\cos 45^\circ + F_2 = \frac{GM^2}{4R^2}(2\sqrt{2}+1)$ .
$\frac{Mv^2}{R} = F \Rightarrow v = \frac{1}{2}\sqrt{\frac{GM}{R}(2\sqrt{2}+1)}$ .
So the answer is (b).

Report a mistake

More questions on Satellites - Orbital Velocity & Period

Four identical particles of equal masses 1 kg made to move along the circumference of a…JEE Main 2021 (24 Feb, Shift 1)
Two stars of masses m and 2m at a distance d rotate about their common centre of mass in…JEE Main 2021 (24 Feb, Shift 1)
The mass density of a spherical galaxy varies as K/r over a large distance ‘r’ from its…JEE Main 2020 (2 Sep, Shift 1)
A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that…JEE Main 2019 (10 Apr, Shift 2)
The time period of a geostationary satellite is 24 h, at a height 6RE ( RE is radius of…NEET 2019
A test particle is moving in a circular orbit in the gravitational field produced by a…JEE Main 2019 (9 Apr, Shift 2)
Four identical particles of mass M are located at the corners of a square of side 'a'…JEE Main 2019 (8 Apr, Shift 1)
A particle is moving with a uniform speed in a circular orbit of radius R in a central…JEE Main 2018

Satellites - Orbital Velocity & Period question from JEE Main 2021 (1 Sep, Shift 2)

More questions on Satellites - Orbital Velocity & Period