Consider a circle of radius $42\  cm$. An insect crawls with uniform speed of $1.3\  cm/s$ along the chord $AB$ then along the circular arc $BCD$ to reach point $D$ and then following cord $DA$ to reach finally $A$. Time spend by the insect to crawl from $A$ to $A$ is closest to    ......... $\sec$

A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular velocity of string when the tension in the string at the top is zero  ........ $rad/sec$

A huge circular arc of length $4.4$ $ly$ subtends an angle $'4 {s}'$ at the centre of the circle. How long it would take for a body to complete $4$ revolution if its speed is $8 \;AU\;per\, second \;?$

Given : $1\, {ly}=9.46 \times 10^{15} \,{m},$ $\, {AU}=1.5 \times 10^{11}\, {m}$

In circular motion, the centripetal acceleration is given by

A ball of mass $0.5 \mathrm{~kg}$ is attached to a string of length $50 \mathrm{~cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \mathrm{~N}$. The maximum possible value of angular velocity of the ball in rad/s is,:

A particle revolves round a circular path. The acceleration of the particle is