$A$ motorcycle is travelling on a curved track of radius $500\,m$. If the coefficient of friction between the road and tyres is $0.5$,the maximum speed to avoid skidding will be ....... $m/s$. (Take $g = 10\,m/s^2$)

$A$ child starts running from rest along a circular track of radius $r$ with constant tangential acceleration $a$. After time $t$,the child feels that the shoes have started slipping on the ground. What is the coefficient of friction $\mu$ between the shoes and the ground? $[g = \text{acceleration due to gravity}]$

Is the maximum safe speed of a vehicle on a banked curved road higher or lower than on a flat curved road?

$A$ car moving on a horizontal road may be thrown out of the road when taking a turn due to:

The maximum velocity (in $m/s$) with which a car driver must traverse a flat curve of radius $150\, m$ and coefficient of friction $0.6$ to avoid skidding is ........ $m/s$.

$A$ 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: