A cyclist moves in a circular track of radius $100$ m. If the coefficient of friction is $0.2$, then the maximum velocity with which the cyclist can take the turn with leaning inwards is ...... $m/s$ 

An aircraft executes a horizontal loop at a speed of $720\; km/h$ with its wings banked at $15^o$. What is the radius of the loop in $km$?

A stone tied to a string is rotated in a circle. If the string is cut, the stone flies away from the circle because

A stone of mass of $16\, kg$ is attached to a string $144 \,m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16$ Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be ....... $ms^{-1}$

A mass of $2 \,kg$ is whirled in a horizontal circle by means of a string at an initial speed of $5$ revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly ....... $rpm$

A body of mass $m$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is one centimetre. If the angular velocity is doubled, the elongation in the spring is $5\, cm$ . The original length of the spring is ............ $cm$