$A$ block $B$,lying on a table,has weight $w$. The coefficient of static friction between the block and the table is $\mu$. Assume that the cord between $B$ and the knot is horizontal. The maximum weight of the block $A$ for which the system will be stationary is

Can the work done by a frictional force be positive or negative?

$A$ pebble of mass $0.05 \, kg$ is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,$(a)$ during its upward motion,$(b)$ during its downward motion,$(c)$ at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of $45^{\circ}$ with the horizontal direction? Ignore air resistance.

$A$ rough inclined plane $BCE$ of height $\left(\frac{25}{6}\right) \text{ m}$ is kept on a rectangular wooden block $ABCD$ of height $10 \text{ m}$,as shown in the figure. $A$ small block is allowed to slide down from the top $E$ of the inclined plane. The coefficient of kinetic friction between the block and the inclined plane is $\frac{1}{8}$ and the angle of inclination of the inclined plane is $\sin^{-1}(0.6)$. If the small block finally reaches the ground at a point $F$,then $DF$ will be (Acceleration due to gravity,$g=10 \text{ ms}^{-2}$)

$Assertion$ : $A$ man and a block rest on a smooth horizontal surface. The man holds a rope which is connected to the block. The man cannot move on the horizontal surface.
$Reason$ : $A$ man standing at rest on a smooth horizontal surface cannot start walking due to the absence of friction (The man is only in contact with the floor as shown).

$A$ mass $2 \sqrt{3} \,kg$ is acted upon by two forces which are inclined to each other at $60^{\circ}$ and each of magnitude $1 \,N$. The acceleration of that mass in $SI$ system is $\left[\sin 30^{\circ}=\cos 60^{\circ}=0.5\right]$ (in $\,m / s^{2}$)