A string of length $0.1\,m$ cannot bear a tension more than $100\,N$. It is tied to a body of mass $100\,g$ and rotated in a horizontal circle. The maximum angular velocity can be .......... $rad/sec$

A particle is released on a vertical smooth semicircular track from point $X$ so that $OX$ makes angle $\theta $ from the vertical ( see figure). The normal reaction of the track on the particle vanishes at point $Y$ where $OY$ makes angle $\phi $ with the horizontal. Then

A stone tied to the end of a string $80\; cm$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\; s$, what is the magnitude and direction of acceleration of the stone ?

Four particles $A, B, C$ and $D$ are moving with constant speed $v$ each. At the instant shown relative velocity of $A$ with respect to $B, C$ and $D$ are in directions

A body is moving on a circle of radius $80 \,m$ with a speed $20 \,m / s$ which is decreasing at the rate $5 \,m / s ^2$ at an instant. The angle made by its acceleration with its velocity is ..........

The radius of circle the period of revolution initial position and sense of revolution are indicated in the figure.

$y-$projection of the radius vector of rotating particle $\mathrm{P}$ is