$A$ car of mass $800 \, kg$ moves on a circular track of radius $40 \, m$. If the coefficient of friction is $0.5$,then the maximum velocity with which the car can move is ......... $m/s$.

$A$ motor vehicle of mass $1000 \,kg$ is moving on a circular road having a banking angle of $30^{\circ}$ and a coefficient of friction of $0.2$. Then the normal reaction force on the motor vehicle is about (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,N$)

$A$ string just breaks under a load of $50 \ kg$. $A$ mass of $1 \ kg$ is attached to one end of this string $10 \ m$ long and is rotated in a horizontal circle. Calculate the greatest number of revolutions that the mass can make in one second without breaking the string. (Take $g = 10 \ m/s^2$)

$A$ modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v$. If the coefficient of static friction between the tyres and the track is $\mu_{s},$ then the magnitude of negative lift $F_{L}$ acting downwards on the car is (Assume forces on the four tyres are identical and $g =$ acceleration due to gravity)

$A$ vehicle is moving with a velocity $v$ on a curved road of width $b$ and radius of curvature $R$. For counteracting the centrifugal force on the vehicle,the difference in elevation required between the outer and inner edges of the road is

$A$ 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