The maximum speed of a car on a road turn of radius $30\,m$; if the coefficient of friction between the tyres and the road is $0.4$; will be ........ $m/s$. (in $.84$)

$A$ body of mass $200 \text{ g}$ is tied to a spring of spring constant $12.5 \text{ N/m}$,while the other end of the spring is fixed at point '$O$'. If the body moves about '$O$' in a circular path on a smooth horizontal surface with a constant angular speed of $5 \text{ rad/s}$,then the ratio of the extension in the spring to its natural length will be:

$A$ vehicle is moving with speed $v$ on a curved road of radius $r$. The coefficient of friction between the vehicle and the road is $\mu$. The angle $\theta$ of banking needed is given by

$A$ car of mass $1500 \ kg$ is moving with a speed of $12.5 \ m/s$ on a circular path of radius $20 \ m$ on a level road. What should be the coefficient of friction between the car and the road,so that the car does not slip?

$A$ cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed,the tendency to overturn is

$A$ cyclist leans at an angle of $30^{\circ}$ with the vertical while negotiating a circular road of radius $20 \sqrt{3} \,m$. The speed of the cycle should be