A 20 ton truck is travelling along a curved path of radius 240 m . If the centre of gravity of the truck above the ground is 2 m and the distance between its wheels is 1.5 m , the maximum speed of the truck with which it can travel without toppling over is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A car is moving on circular track banked at an angle of $45^{\circ}$. If the maximum permissible speed of the car to avoid slipping is twice the optimum speed of the car to avoid the wear and tear of the tyres, then the coefficient of static friction between the wheels of the car and the road is

If the radii of circular path of two particles of same mass are in the ratio of $1: 2$, then to have a constant centripetal force, the ratio of their speeds should be

A car is travelling with linear velocity $v$ on a circular road of radius $r$. If its velocity is increasing at a rate of $a \mathrm{~ms}^{-2}$, then the resultant acceleration will be