$A$ bullet of mass $20 \, g$ travelling horizontally with a speed of $500 \, m/s$ passes through a wooden block of mass $10.0 \, kg$ initially at rest on a surface. The bullet emerges with a speed of $100 \, m/s$ and the block slides $20 \, cm$ on the surface before coming to rest. Find the coefficient of friction between the block and the surface. $(g = 10 \, m/s^2)$

$A$ horizontal force $12 \, N$ pushes a block weighing $1/2 \, kg$ against a vertical wall. The coefficient of static friction between the wall and the block is $0.5$ and the coefficient of kinetic friction is $0.35$. Assuming that the block is not moving initially,which one of the following choices is correct? (Take $g = 10 \, m/s^2$)

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium,the angle $\theta$ should be ........ $^o$.

The mass of a hydrogen molecule is $3.32 \times 10^{-27} \ kg$. If $10^{23}$ hydrogen molecules strike,per second,a fixed wall of area $2 \ cm^2$ at an angle of $45^\circ$ to the normal,and rebound elastically with a speed of $10^3 \ m/s$,then the pressure on the wall is nearly:

$A$ block of mass $0.18 \ kg$ is attached to a spring of force-constant $2 \ N/m$. The coefficient of friction between the block and the floor is $0.1$. Initially,the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of $0.06 \ m$ and comes to rest for the first time. The initial velocity of the block in $m/s$ is $v = N/10$. Then $N$ is:

Fill in the blanks:
$(a)$ $A$ load of $3 \, kg$ is suspended from a rope of $6 \, kg$. The tension at the top end of the rope is ...........
$(b)$ The effect produced by a force $F$ acting for a time $\Delta t$ is the same as that produced by a force $2F$ acting for a time ...........
$(c)$ Friction ........... due to excessive ironing.