A car travels on a circular racetrack of radius 50 m , which is banked at an angle $\theta$. If the car travels at a speed $10 \mathrm{~ms}^{-1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be $10 \mathrm{~ms}^{-2}$, the value of $\theta$ is:

A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12 . Keeping the box in stationary state over the trolley, the maximum acceleration with which the trolley can be moved horizontally in $\mathrm{m} \mathrm{s}^{-2}$ is:

$$ \left(g=10 \mathrm{~m} / \mathrm{s}^2\right) $$

The magnitude and direction of the acceleration produced in a body of mass 5 kg when two mutually perpendicular forces 8 N and 6 N act on it, are respectively:

There are two inclined surfaces of equal length $(L)$ and same angle of inclination $45^{\circ}$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction $\left(\mu_k\right)$ between the object and the rough surface is close to