A stone ties to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44$ seconds, what is the magnitude and direction of acceleration of the stone
$\frac{{{\pi ^2}}}{4}\;m{s^{ - 2}}$ and direction along the radius towards the centre
${\pi ^2}\;m{s^{ - 2}}$ and direction along the radius away from the centre
${\pi ^2}\;m{s^{ - 2}}$ and direction along the radius towards the centre
${\pi ^2}\;m{s^{ - 2}}$ and direction along the tangent to the circle
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 ........ $N$
If the equation for the displacement of a particle moving on a circular path is given by $(\theta) = 2t^3 + 0.5$, where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particle after $2\, sec$ from its start is ......... $rad/sec$
A simple pendulum consisting of a mass $M$ attached to a string of length $L$ is released from rest at an angle $\alpha$. $A$ pin is located at a distance $l$ below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle $\theta$ which string makes with the vertical after hitting the pin is :-
A particle moves in a circle of radius $5 \;cm$ with constant speed and time period $0.2 \pi\; sec$. The acceleration of the particle is .... $m/sec^2$
Roads are banked on curves so that