Question

Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is (A) $\sqrt{\frac{G M}{R}}$ (B) $\sqrt{2 \sqrt{2} \frac{G M}{R}}$ (C) $\sqrt{\frac{G M}{R}(1+2 \sqrt{2})}$ (D) $\frac{1}{2} \sqrt{\frac{G M}{R}(1+2 \sqrt{2})}$

Name: Problem 87, Chapter 7: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-02T07:38:11-08:00
Duration: 2 min 16 s
Channel: Khoobchandra Agrawal
Description: Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is (A) √((G M)/(R)) (B) √(2 √(2) (G M)/(R)) (C) √((G M)/(R)(1+2 √(2))) (D) (1)/(2) √((G M)/(R)(1+2 √(2)))

   Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is
(A) $\sqrt{\frac{G M}{R}}$
(B) $\sqrt{2 \sqrt{2} \frac{G M}{R}}$
(C) $\sqrt{\frac{G M}{R}(1+2 \sqrt{2})}$
(D) $\frac{1}{2} \sqrt{\frac{G M}{R}(1+2 \sqrt{2})}$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 7, Problem 87

Instant Answer

Solved by Expert Khoobchandra Agrawal

10/02/2021

Step 1

The diagonal of the square, which is the distance between any two particles, is $x = 2R\sqrt{2}$. Show more…

Show all steps

Thanks for your feedback!

Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is (A) $\sqrt{\frac{G M}{R}}$ (B) $\sqrt{2 \sqrt{2} \frac{G M}{R}}$ (C) $\sqrt{\frac{G M}{R}(1+2 \sqrt{2})}$ (D) $\frac{1}{2} \sqrt{\frac{G M}{R}(1+2 \sqrt{2})}$

Play audio

Feedback

Khoobchandra Agrawal and 57 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Newton's Law of Universal Gravitation

This law states that every two masses attract one another with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. It is crucial in calculating the gravitational forces present in a system of masses.

Centripetal Force in Circular Motion

To keep a body moving in a circle at a constant speed, its net inward force must equal the centripetal force needed to change the direction of its velocity. In gravitational systems, components of the gravitational attractions often sum to provide this necessary centripetal force.

Symmetry in Gravitational Systems

When masses are arranged symmetrically, such as being equally spaced on a circle, their individual gravitational forces can be combined using vector addition. This symmetry simplifies the analysis by reducing the complexity of the net force calculations needed to determine the dynamics of the system.

Please give Ace some feedback