A monkey of mass $m$ is climbing a rope hanging from the roof with acceleration $a$. The coefficient of static friction between the body of the monkey and the rope is $\mu$. Find the direction and value of friction force on the monkey.

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 conveyor belt is moving at a constant speed of $2\, ms^{-1}$. A box is gently dropped on it. The coefficient of friction between them is $\mu  = 0.5$. The distance that the box will move relative to belt before coming to rest on it, (taking $g = 10\, ms^{-2}$) is  ........  $m$.

The tension $T$ in the string shown in figure is

In the figure, a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_1$ and that between the floor and the ladder is $\mu_2$. The normal reaction of the wall on the ladder is $N_1$ and that of the floor is $N_2$. If the ladder is about to slip, then

$Image$

$(A)$ $\mu_1=0 \mu_2 \neq 0$ and $N _2 \tan \theta=\frac{ mg }{2}$

$(B)$ $\mu_1 \neq 0 \mu_2=0$ and $N_1 \tan \theta=\frac{m g}{2}$

$(C)$ $\mu_1 \neq 0 \mu_2 \neq 0$ and $N _2 \tan \theta=\frac{ mg }{1+\mu_1 \mu_2}$

$(D)$ $\mu_1=0 \mu_2 \neq 0$ and $N _1 \tan \theta=\frac{ mg }{2}$

A car is moving with uniform velocity on a rough horizontal road. Therefore, according to Newton's first law of motion