A particle is moving with uniform speed along | vedclass

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

Question

(A) The centripetal force required for circular motion is provided by the central force $F$. Given $F \propto \frac{1}{R^{3}}$,we can write $F = \frac

Vedclass · Accepted Answer

$T \propto R^{2}$

Vedclass · Answer

(A) The centripetal force required for circular motion is provided by the central force $F$. Given $F \propto \frac{1}{R^{3}}$,we can write $F = \frac{K}{R^{3}}$,where $K$ is a constant.For a particle of mass $m$ moving with angular velocity $\omega$ in a circle of radius $R$,the centripetal force is $F = m \omega^{2} R$.Equating the two expressions: $\frac{K}{R^{3}} = m \omega^{2} R$.Rearranging for $\omega^{2}$: $\omega^{2} = \frac{K}{m R^{4}}$.Since the time period $T = \frac{2 \pi}{\omega}$,we have $\omega = \frac{2 \pi}{T}$.Substituting this into the equation: $(\frac{2 \pi}{T})^{2} = \frac{K}{m R^{4}}$.This simplifies to $\frac{4 \pi^{2}}{T^{2}} = \frac{K}{m R^{4}}$,which implies $T^{2} \propto R^{4}$.Taking the square root of both sides,we get $T \propto R^{2}$.

$A$ particle is moving with uniform speed along the circumference of a circle of radius $R$ under the action of a central fictitious force $F$ which is inversely proportional to $R^{3}$. Its time period of revolution will be given by

Similar Questions

$A$ ball of mass $m$ is attached to the free end of an inextensible string of length $\ell$. Let $T$ be the tension in the string. The ball is moving in a horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be

$A$ motorcycle driver doubles their velocity when taking a turn. The force exerted outwardly will be

$A$ $500 \,kg$ car takes a round turn of radius $50 \,m$ with a velocity of $36 \,km/h$. The centripetal force is (in $\,N$)

$A$ car of mass $m$ passes over the top of a convex bridge of radius of curvature $r$ with a velocity $v$. What is the normal force exerted by the bridge on the car?

$A$ wire of length $2.5 \ m$ is fixed at one end and a box of mass $4 \ kg$ is tied at the other end. If the wire rotates in a horizontal circle about the fixed end with $\frac{2}{\pi} \ rev/s$ rotations per second,then the tension in the wire is (in $N$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module