Two particles each of mass m are placed at po | vedclass

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

Question

(C) Let the distance $RS = x$. From the figure,$RS = l$. The distance from $P$ to $S$ is $PS = \sqrt{PR^2 + RS^2} = \sqrt{(l/2)^2 + l^2} = \sqrt{l^2/4

Vedclass · Accepted Answer

$\frac{16 G m^2}{5 \sqrt{5} l^2}$

Vedclass · Answer

(C) Let the distance $RS = x$. From the figure,$RS = l$. The distance from $P$ to $S$ is $PS = \sqrt{PR^2 + RS^2} = \sqrt{(l/2)^2 + l^2} = \sqrt{l^2/4 + l^2} = \sqrt{5l^2/4} = \frac{\sqrt{5}}{2} l$.The gravitational force exerted by particle at $P$ on particle at $S$ is $F_1 = \frac{G m^2}{PS^2} = \frac{G m^2}{5l^2/4} = \frac{4 G m^2}{5 l^2}$.Similarly,the gravitational force exerted by particle at $Q$ on particle at $S$ is $F_2 = \frac{G m^2}{QS^2} = \frac{4 G m^2}{5 l^2}$.Let $	heta$ be the angle between $RS$ and $PS$. Then $\cos 	heta = \frac{RS}{PS} = \frac{l}{(\sqrt{5}/2) l} = \frac{2}{\sqrt{5}}$.The horizontal components of the forces $F_1$ and $F_2$ cancel each other out. The resultant force is the sum of the vertical components:$F = F_1 \cos 	heta + F_2 \cos 	heta = 2 F_1 \cos 	heta$.Substituting the values:$F = 2 	imes \left( \frac{4 G m^2}{5 l^2} ight) 	imes \left( \frac{2}{\sqrt{5}} ight) = \frac{16 G m^2}{5 \sqrt{5} l^2}$.

Two particles each of mass $m$ are placed at points $P$ and $Q$ as shown in the figure. $R$ is the mid-point of $PQ = l$. The gravitational force on the third particle of mass $m$ placed at point $S$ on the perpendicular bisector of $PQ$ is

Similar Questions

The gravitational force between two identical uniform solid gold spheres of radius $r$ placed in contact is proportional to:

Consider an infinite distribution of point masses (each of mass $m$) placed on the $x$-axis as shown in the diagram. What is the gravitational force acting on the point mass placed at the origin?

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

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

Vedclass Test Series

Exam Paper Generator

Online Exam Module