$A$ 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 $g = 10\,m/s^2$)

$A$ 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

$A$ cyclist moves on 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 while leaning inwards is ...... $m/s$.

$A$ motorcyclist moving with a velocity of $72\, km/h$ on a flat road takes a turn at a point where the radius of curvature of the road is $20\, m$. The acceleration due to gravity is $10\, m/s^2$. In order to avoid skidding,he must not bend with respect to the vertical plane by an angle greater than

If the coefficient of friction between the tires and the road is $\mu$,the maximum safe speed is $10\;m/s$. If the coefficient of friction becomes $\mu' = \frac{\mu}{2}$,what will be the new maximum safe speed?

The normal reaction $N$ for a vehicle of $800 \, kg$ mass,negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is $... \times 10^{3} \, kg \cdot m/s^{2}$. [Given $\cos 30^{\circ} = 0.87, \mu_{s} = 0.2$]