$A$ clock has $75 \ cm$ and $60 \ cm$ long second hand and minute hand respectively. In $30$ minutes duration,the tip of the second hand will travel $x$ distance more than the tip of the minute hand. The value of $x$ in meters is nearly (Take $\pi = 3.14$):

$A$ wheel rotates with an angular acceleration of $3 \ rad \ s^{-2}$ and an initial angular velocity of $2 \ rad \ s^{-1}$. What will be its angular displacement after $2 \ s$?

$A$ particle is revolving in a circular path of radius $25 \, m$ with a constant angular speed of $12 \, rev/min$. The angular acceleration of the particle is .......... $rad/s^2$.

$A$ particle at rest starts moving with constant angular acceleration '$\alpha$' in a circular path of radius '$r$'. At a certain instant, the magnitude of centripetal acceleration is $(1/3)^{rd}$ the tangential acceleration. The relation between linear speed $(V)$ and angular acceleration $(\alpha)$ is

$A$ merry-go-round makes $120$ revolutions per minute. $A$ child sitting on it starts crying,so the merry-go-round is slowed down with a retardation of $2 \ rad \ s^{-2}$. How long will it take for the merry-go-round to come to a stop? How many revolutions will it make before coming to a stop?

Three particles $A, B$ and $C$ move in a circle of radius $r = \frac{1}{\pi} \, m$ in the anticlockwise direction with speeds $1 \, m/s$,$2.5 \, m/s$ and $2 \, m/s$ respectively. The initial positions of $A, B$ and $C$ are as shown in the figure. The ratio of the distance travelled by $B$ and $C$ by the instant $A, B$ and $C$ meet for the first time is