$A$ 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 $\,N$)

$A$ car is moving along a circular path having a coefficient of friction $0.5$ and a radius of curvature $16.2 \,m$. The maximum velocity of the car that can travel without skidding outwards is (Acceleration due to gravity $= 10 \,ms^{-2}$)

$A$ stone of mass $0.25 \; kg$ tied to the end of a string is whirled round in a circle of radius $1.5 \; m$ with a speed of $40 \; rev./min$ in a horizontal plane. What is the tension in the string? What is the maximum speed in $m/s$ with which the stone can be whirled around if the string can withstand a maximum tension of $200 \; N$ (in $; m/s$)?

$A$ cyclist is travelling with velocity $v$ on a curved road of radius $R$. The angle $\theta$ through which the cyclist leans inwards is given by

$A$ car when passing through a convex bridge exerts a force on it which is equal to:

$A$ particle is moving along the circle $x^2 + y^2 = a^2$ in an anticlockwise direction. The $x-y$ plane is a rough horizontal stationary surface. At the point $(a \cos \theta, a \sin \theta)$,the unit vector in the direction of friction on the particle is: