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 $\cos 30^{\circ} = 0.87, \mu_{s} = 0.2$]

$A$ $100 \, kg$ car is moving with a maximum velocity of $9 \, m/s$ across a circular track of radius $30 \, m$. The maximum force of friction between the road and the car is ........ $N$.

$A$ car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is $\mu_s$. The maximum safe velocity on this road is

$A$ particle describes a horizontal circle on the smooth inner surface of a cone as shown in the figure. If the height of the circle above the vertex is $10 \ cm$,find the speed of the particle. (Given: acceleration due to gravity $g = 10 \ m/s^2$ and assume the semi-vertical angle $\theta = 45^\circ$ based on the geometry of the cone). (in $m/s$)

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?

For a body moving in a circular path,what is the condition for no skidding if $\mu$ is the coefficient of friction?