A particle of mass ${m}$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that ${r}=\frac{{L}}{\sqrt{2}}$. The speed of particle will be:

A stone tied to $180 cm$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{ x }\,ms ^{-2}$. The value of $x.........\left(\text { Take } \pi=\frac{22}{7}\right)$

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 is in uniform circular motion, then its velocity is perpendicular to

A wheel completes $2000$ revolutions to cover the $9.5\, km$. distance. then the diameter of the wheel is

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