Embibe Experts Solutions for Chapter: Circular Motion, Exercise 2: Exercise-2

The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as, $k=a{s}^2$, where $a$ is a constant. The force acting on the particle is,

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c=k^{2}r{t}^2$, where $k$ is a constant. The power delivered to the particle by the forces acting on it is

A particle moves along a circle of radius $\left(\frac{20}{\pi }\right) \mathrm{m}$ with constant tangential acceleration. If the speed of the particle is $80 \mathrm{m}/\mathrm{s}$ at the end of the second revolution after motion has begun, the tangential. acceleration is:

Centrifugal force is an inertial force when considered by -

A rod of length $L$ is pivoted at one end and is rotated with a uniform angular velocity, in a horizontal plane. Let $T_1$ and $T_2$ be the tensions at points $\frac{L}{4}$ and $\frac{3L}{4}$, away from the pivoted ends.

When a ceiling fan is switched off, its angular velocity reduces to $50\%$ while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)

If a particle of mass $m$ is moving in a horizontal circle of radius $r$ with a centripetal force $\left(-\frac{K}{r^2}\right)$, total energy is

Assertion: A ball tied by thread is undergoing circular motion (of radius $R$) in a vertical plane. (Thread always remains in vertical plane). The difference of maximum and minimum tension in thread is independent of speed $\left(u\right)$ of ball at the lowest position $(u>\sqrt{5gR}).$
Reason: For a ball of mass $m$ tied by thread undergoing vertical circular motion (of radius $R$ ), difference in maximum and minimum magnitude of centripetal acceleration of the ball is independent of speed $\left(u\right)$ of ball at the lowest position $(u>\sqrt{5gR}).$