A boy is sitting on the horizontal platform of a joy wheel at a distance of $5 \,m$ from the center. The wheel begins to rotate and when the angular speed exceeds $1 \,rad / s$, the boy just slips. The coefficient of friction between the boy and the wheel is $\left(g=10 \,m / s ^2\right)$

A curved in a level road has a radius $75\, m$. The maximum speed of a car turning this curved road can be $30 \,m / s$ without skidding. If radius of curved road is changed to $48\, m$ and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be .........$m / s$.

Assuming the coefficient of friction between the road and tyres of a car to be $0.5$, the maximum speed with which the car can move round a curve of $40.0\, m$ radius without slipping, if the road is unbanked, should be ......... $m/s$

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

If the radius of curvature of the path of two particles of same mass are in the ratio $3:4,$ then in order to have constant centripetal force, their velocities will be in the ratio of:

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 .......... $m/sec$