Three particles each of mass M are placed at | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the equilateral triangle be $PQR$ with side length $l$. The masses $M$ are at $P, Q,$ and $R$. The mass $m$ is placed at the midpoint $L$ of s

Vedclass · Accepted Answer

$\frac{4GMm}{3l^2}$

Vedclass · Answer

(B) Let the equilateral triangle be $PQR$ with side length $l$. The masses $M$ are at $P, Q,$ and $R$. The mass $m$ is placed at the midpoint $L$ of side $QR$.The gravitational force exerted by the mass $M$ at $Q$ on mass $m$ at $L$ is $F_Q = \frac{GMm}{(l/2)^2}$ directed towards $Q$.The gravitational force exerted by the mass $M$ at $R$ on mass $m$ at $L$ is $F_R = \frac{GMm}{(l/2)^2}$ directed towards $R$.Since $F_Q$ and $F_R$ are equal in magnitude and opposite in direction,they cancel each other out $(F_Q + F_R = 0)$.The net force on $m$ is therefore only due to the mass $M$ at vertex $P$.The distance $PL$ is the altitude of the equilateral triangle,given by $PL = l \sin 60^{\circ} = l \frac{\sqrt{3}}{2}$.The magnitude of the force is $F = \frac{GMm}{(PL)^2} = \frac{GMm}{(l\sqrt{3}/2)^2} = \frac{GMm}{3l^2/4} = \frac{4GMm}{3l^2}$.

Three particles each of mass $M$ are placed at the three corners of an equilateral triangle of side $l$. What is the gravitational force due to this system of particles on another particle of mass $m$ placed at the midpoint of any side?

Similar Questions

The tidal waves in the sea are primarily due to

The distance between the centres of the moon and the earth is $D$. The mass of the earth is $81$ times the mass of the moon. At what distance from the centre of the earth will the net gravitational force on a test mass be zero?

The gravitational force between a hollow spherical shell (of radius $R$ and uniform density) and a point mass $m$ is $F$. Show the nature of the $F$ versus $r$ graph,where $r$ is the distance of the point mass from the centre of the hollow spherical shell.

Two particles of equal mass $m$ move in a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is

Vedclass Test Series

Exam Paper Generator

Online Exam Module