To avoid slipping while walking on ice,one should take smaller steps because of the

$A$ 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 $g = 10 \, m s^{-2}$]

If the normal force is doubled,the coefficient of friction is

$A$ 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 $ms^{-2}$)

$A$ block of mass $50 \, kg$ can slide on a rough horizontal surface. The coefficient of friction between the block and the surface is $0.6$. The least force of pull acting at an angle of $30^\circ$ to the upward drawn vertical which causes the block to just slide is ........ $N$.

The limiting friction is