$Assertion$ : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.

$Reason$ : The centripetal acceleration in circular motion is dependent on angular velocity of the body.

As shown in the figure, a particle is moving with constant speed $\pi\,m / s$. Considering its motion from $A$ to $B$, the magnitude of the average velocity is:

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 huge circular arc of length $4.4$ $ly$ subtends an angle $'4 {s}'$ at the centre of the circle. How long it would take for a body to complete $4$ revolution if its speed is $8 \;AU\;per\, second \;?$

Given : $1\, {ly}=9.46 \times 10^{15} \,{m},$ $\, {AU}=1.5 \times 10^{11}\, {m}$

A stone tied to the end of a string of $1\, m$ 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?

A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}$, the ratio of instantaneous velocity to its average velocity is $\pi: x \sqrt{2}$. The value of $x$ will be $.........$