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

A pen of mass $m$ is lying on a piece of paper of mass $M$ placed on a rough table. If the coefficients of friction between the pen and paper and the paper and the table are $\mu_1$ and $\mu_2$, respectively. Then, the minimum horizontal force with which the paper has to be pulled for the pen to start slipping is given by

A block weighs $W$ is held against a vertical wall by applying a horizontal force $F$. The minimum value of $F$ needed to hold the block is

A uniform rope lies on a horizontal table so that a part of it hangs over the edge. The rope begins to slide down when the length of the hanging part is $25\%$ of the entire length. The coefficient of friction between the rope and the table is

A small body slips, subject to the force of friction, from point $A$ to point $B$ along two curved surfaces of equal radius, first along route $1,$ then along route $2$. Friction does not depend on the speed and the coefficient of friction on both routes is the same. In which case will the body’s speed at $B$ be greater?

The coefficient of static friction, $\mu _s$ between block $A$ of mass $2\,kg$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of block $B$ so that the two blocks $B$ so that the two blocks do not move? The string and the pulley are assumed to be smooth and masseless ....... $kg$ $(g = 10\,m/s^2)$