If a body describes a circular motion under a | vedclass

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

Question

(C) In an inverse square field,the force $F$ acting on a body of mass $m$ moving in a circular orbit of radius $r$ is given by $F = \frac{k}{r^2}$,whe

Vedclass · Accepted Answer

$T^2 \propto r^3$

Vedclass · Answer

(C) In an inverse square field,the force $F$ acting on a body of mass $m$ moving in a circular orbit of radius $r$ is given by $F = \frac{k}{r^2}$,where $k$ is a constant.For circular motion,this force provides the necessary centripetal force: $\frac{k}{r^2} = \frac{mv^2}{r}$.Simplifying this,we get $v^2 = \frac{k}{mr}$,which implies $v = \sqrt{\frac{k}{mr}}$.The time period $T$ for one revolution is $T = \frac{2\pi r}{v}$.Substituting the expression for $v$: $T = \frac{2\pi r}{\sqrt{\frac{k}{mr}}} = 2\pi \sqrt{\frac{m}{k}} \cdot r^{3/2}$.Squaring both sides,we get $T^2 = 4\pi^2 \frac{m}{k} r^3$.Since $4, \pi, m,$ and $k$ are constants,we have $T^2 \propto r^3$.

If a body describes a circular motion under an inverse square field,the time taken to complete one revolution $T$ is related to the radius of the circular orbit $r$ as:

Similar Questions

An earth satellite $X$ is revolving around the earth in an orbit whose radius is one-fourth of the radius of the orbit of a communication satellite. The time period of revolution of $X$ is ..........

According to Kepler, the period of revolution of a planet $(T)$ and its mean distance from the sun $(r)$ are related by the equation:

The time period of a satellite of the Earth is $5$ hours. If the separation between the Earth and the satellite is increased to four times the previous value,the new time period will become ......... $hours$.

$A$ planet is revolving around the sun in an elliptical path as shown. The orbital velocity of the planet will be minimum at:

The ratio of the distances of two planets from the sun is $1.38$. The ratio of their period of revolution around the sun is

Vedclass Test Series

Exam Paper Generator

Online Exam Module