Embibe Experts Solutions for Chapter: Circular Motion, Exercise 4: Exercise (Previous Year Questions)

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is

A car of mass $1000 \mathrm{kg}$ negotiates a banked curve of radius $90 \mathrm{m}$ on a frictionless road. If banking angle is $45°$, the maximum speed of car is $\left[g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]:$

A car of mass $m$ is moving on a level circular track of radius $R$. If ${\mu }_s$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by

Two stones of masses $m$ and $2\mathrm{m}$ are whirled in horizontal circles, the heavier one in a radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of lighter stone is $n$ times that of the value of heavier stone when they experience the same centripetal force. The value of $n$ is,

A car is negotiating a curved road of radius $R$. The road is banked at an angle $\mathrm{\theta }$. The coefficient of friction between the tyres of the car and the road is ${\mu }_s$. The maximum safe velocity on this road is

In the given figure, $a=15 \mathrm{m} {\mathrm{s}}^{-2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R=2.5 \mathrm{m}$ at a given instant of time. The speed of the particle is

A particle starts with angular acceleration $2 \mathrm{rad} {\mathrm{s}}^{-2}$. It moves $100 \mathrm{rad}$ in a random interval of $5 \sec$. Find out the time at which random interval starts.

One end of the string of length $l$ is connected to a particle of mass $m$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$, the net force on the particle (directed towards the centre) will be ($T$ represents the tension in the string)