Embibe Experts Solutions for Chapter: Circular Motion, Exercise 1: Exercise 1

A train is moving towards north. At one place it turns towards north-east. Here, we observe that:

A particle is moving in uniform circular motion with speed $v$ and radius $R$. The angular acceleration of the particle is:

A brass ball is tied to a thin wire and swung so as to move uniformly in a horizontal circle. Which of the following statements in this regard is/are true?

$1$. The ball moves with constant velocity.

$2$. The ball moves with constant speed.

$3$. The ball moves with constant acceleration.

$4$. The magnitude of the acceleration of the ball is constant.

Select the correct answer using the codes given.

One end of a string of length $\text{'}l\text{'}$ is connected to a particle of mass $\text{'}m\text{'}$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $\text{'}v\text{'}$, the net force on the particle (directed towards the centre is: ($T$ is the tension in the string)

A ball of mass $\left(m\right)$ $0.5 \mathrm{kg}$ is attached to the end of a string having length $\left(L\right)$ $0.5 \mathrm{m}$. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is $324 \mathrm{N}$. The maximum possible value of angular velocity of ball (in $\mathrm{radian} {\mathrm{s}}^{-1}$) is:

A cane filled with water is revolved (with a constant speed) in a vertical circle of radius $4 \mathrm{m}$ and the water just does not fall down.
The time period of revolution will be-

A particle of mass $m$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r=\frac{L}{\sqrt{2}}$. The speed of particle will be :

A bucket tied at the end of a $1.6 \mathrm{m}$ long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position :- (Take $g=10 \mathrm{m} {\sec }^{-2}$)