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

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 .........$m / s$.

A car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$ . The maximum speed with which the car can move without skidding out is

At time $t=0$, a disk of radius $1 m$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} rad s ^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi} s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$ ) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is. . . . . . .[Take $g=10 m s ^{-2}$.]

A cyclist on a level road takes a sharp circular turn of radius $3 \;m \;\left( g =10 \;ms ^{-2}\right)$. If the coefficient of static friction between the cycle tyres and the road is $0.2$, at which of the following speeds will the cyclist not skid while taking the turn?

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20\, m.$ The speed of the car at the top of the hill is between