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

A block of mass $m$ is pressed against a vertical surface by a spring of unstretched length $l$ . If the coefficient of friction between the block and the surface is $\mu $. Choose the correct statement.

A uniform chain of length $L$ changes partly from a table which is kept in equilibrium by friction. The maximum length that can withstand without slipping is $l$, then coefficient of friction between the table and the chain is

A man pulls a block heavier than himself with a light horizontal rope. The coefficient of friction is the same between the man and the ground, and between the block and the ground

A mass of $4\; kg$ rests on a horizontal plane. The plane is gradually inclined until at an angle $\theta= 15^o$ with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface ?

A block of mass $m$ (initially at rest) is sliding up (in vertical direction) against a rough vertical wall with the help of a force $F$ whose magnitude is constant but direction is changing. $\theta  = {\theta _0}t$  where $t$ is time in sec. At $t$ = $0$ , the force is in vertical upward direction and then as time passes its direction is getting along normal, i.e., $\theta  = \frac{\pi }{2}$ .The value of $F$ so that the block comes to rest when $\theta  = \frac{\pi }{2}$ , is