Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Circular Motion, Exercise 2: Critical Thinking

Assertion: For looping a vertical loop of radius $r,$ the minimum velocity at the lowest point should be $\sqrt{5\mathrm{gr}}$

Reason: Velocity at the highest point would be zero.

A flywheel at rest is reached to an angular velocity of $36 \mathrm{rad} {\mathrm{s}}^{-1}$ in $6 \mathrm{s}$ with a constant angular acceleration. The total angle turned during this interval is

An engine requires $5 \mathrm{s}$ to go from a speed of $600 \mathrm{rpm}$ to $1200 \mathrm{rpm}$ with constant acceleration. How many revolutions does it make in this period?

A wheel of a vehicle is rotated to a uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates through an angle ${\theta }_1$ in the first $2 \mathrm{s}$ and in the next $3 \mathrm{s},$ it rotates through an additional angle ${\theta }_2.$The ratio of $\frac{{\theta }_2}{{\theta }_1}$ is

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)

A particle is moving in a circle of radius $r$ centered at $O$ with constant speed $v.$ What is the change in velocity in moving from $A$ to $B$ if $\angle \mathrm{AOB}=60°?$

A particle moves along a circle of radius $\frac{20}{\mathrm{\pi }} \mathrm{m}$ with a constant tangential acceleration. If the velocity of the particle is $80 \mathrm{m} {\mathrm{s}}^{-1}$ at the end of the $2^{\mathrm{nd}}$ revolution after motion has begun, the tangential acceleration is

A stone of mass $1 \mathrm{kg}$ tied to a light inextensible string of length $\left(10/3\right) \mathrm{m}$ is whirling in a circular path in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension is $4$ and if $g$ is taken to be $10 \mathrm{m} {\mathrm{s}}^{-2},$the speed of the stone at the highest point of the circle is