A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $9 \mathrm{~m}$ and completes $120$ revolutions in $3$ minutes. The magnitude of centripetal acceleration of monkey is (in $\mathrm{m} / \mathrm{s}^2$ ):

Two particles $A$ and $B$ start at the origin $O$ and travel in opposite directions along the circular path at constant speeds $0.5\,m/s$ and $1.5\,m/s$ , respectively. The time when they collide with each other ........ $\sec$

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

An aircraft executes a horizontal loop with a speed of $150\, m/s$ with its wings banked at an angle of $12^o$. The radius of the loop is ..........  $km$ $(g = 10\, m/s^2 \; and\; \tan 12^o = 0.2125)$

A particle is moving in a circular path of radius $r$ under the action of a force $F$. If at an instant velocity of particle is $v$, and speed of particle is increasing, then

A car is moving with a uniform speed on a level road. Inside the car there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn maintaining the speed on the level road. The balloon in the car will