A particle $P$ is moving in a circle of radius $'a'$ with a uniform speed $v$ . $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$ the angular velocity of $P$ about $A$ and $C$ are in the ratio 

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 string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $2/\pi$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

A car is travelling with linear velocity $v$ on a circular road of radius $r$. If it is increasing its speed at the rate of $'a'$ $meter/{\sec ^2}$, then the resultant acceleration will be

The centripetal acceleration is given by

If the length of the second's hand in a stop clock is $3 \,cm$ the angular velocity and linear velocity of the tip is