$A \,10\, kg$ ball attached to the end of a rigid massless rod of length $1\, m$ rotates at constant speed in a horizontal circle of radius $0.5\, m$ and period $1.57 \, sec$ as in fig. The force exerted by rod on the ball is ........ $N$.

A ball of mass $0.1$ kg is suspended by a string. It is displaced through an angle of ${60^o}$ and left. When the ball passes through the mean position, the tension in the string is ........ $N$

A boy ties a stone of mass $100 \,g$ to the end of a $2$ $m$ long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of $80 \,N$. If the maximum speed with which the stone can revolve is $\frac{ K }{\pi} rev$. / $min$. The value of $K$ is (Assume the string is massless and unstretchable)

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that  

What is uniform circular motion ? By using proper figure, obtain equation of acceleration ${a_c}\, = \,\frac{{{v^2}}}{r}$ for uniform circular motion. Show that its direction is towards centre.

The second's hand of a watch has length $6\,\, cm$. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be