$A$ box of mass $2 kg$ is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. The coefficient of static friction between the box and the roof of the car is $0.2$ and $g=10 ms^{-2}$. This maximum acceleration of the car,for the box to remain stationary,is: (in $ms^{-2}$)

$A$ body of mass $5 \,kg$ is placed on a rough horizontal surface of coefficient of static friction $\frac{1}{3}$. The least pulling force to be applied on the body at an angle $45^{\circ}$ with the horizontal to slide it,is . . . . . . $\left(g=10 \,ms^{-2}\right)$

Write the unit of the coefficient of static friction.

$A$ man walks over a rough surface; the angle between the force of friction and the instantaneous velocity of the person is

Given below are two statements:
$Statement$ $(I)$: The limiting force of static friction depends on the area of contact and is independent of materials.
$Statement$ $(II)$: The limiting force of kinetic friction is independent of the area of contact and depends on materials.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ body of mass $1 \, kg$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $F \, N$. The value of $F$ will be (Nearest Integer). [Take $g = 10 \, m s^{-2}$]