$A$ horizontal force $F = mg/3$ is applied on the upper surface of a uniform cube of mass $m$ and side $a$,which is resting on a rough horizontal surface having $\mu_S = 1/2$. The distance between the lines of action of $mg$ and the normal reaction $N$ is:

Fill in the blanks:
$(a)$ The friction acting on both wheels of a moving bicycle is in the ..... direction.
$(b)$ Friction depends on the ........... and ........ of the contact surfaces.
$(c)$ The necessary condition for parking a vehicle on a banked,curved road is ...........
$(d)$ The time rate of change of momentum gives the physical quantity ...........

At time $t=0$, a force $F=\alpha t$, where $t$ is time in seconds, is applied to a body of mass $1 \text{ kg}$, resting on a smooth horizontal plane. If the direction of the force makes an angle of $45^{\circ}$ with the horizontal, then the velocity of the body at the moment of its breaking off the plane is

In the shown arrangement,if $f_A$,$f_B$ and $T$ are the frictional forces on block $A$,block $B$ and the tension in the string respectively,then their values are:

In which of the following graphs,the total change in momentum is zero?

$A$ disc of mass $100 \,g$ slides down from rest on an inclined plane of $30^{\circ}$ and comes to rest after travelling a distance of $1 \,m$ along the horizontal plane. If the coefficient of friction is $0.2$ for both inclined and horizontal planes, then the work done by the frictional force over the whole journey, approximately, is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,J$)