$A$ $0.5\, kg$ ball moving with a speed of $12\, m/s$ strikes a hard wall at an angle of $30^\circ$ with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for $0.25\, s$,the average force acting on the wall is ........... $N$.

$A$ body of mass $2 \ kg$ is acted upon by two forces each of magnitude $1 \ N$ and inclined at $60^{\circ}$ with each other. The acceleration of the body in $m/s^2$ is $[\cos 60^{\circ}=0.5]$

In the arrangement shown in the figure,the masses of blocks $B$ and $A$ are $2m$ and $m$ respectively. The surface between $B$ and the floor is smooth. Block $B$ is connected to block $C$ by means of a string-pulley system. If the whole system is released,find the minimum value of the mass of block $C$ so that block $A$ remains stationary with respect to $B$. The coefficient of friction between $A$ and $B$ is $\mu$.

Two bodies $A$ and $B$ of masses $5 \, kg$ and $10 \, kg$ in contact with each other rest on a table against a rigid wall. The coefficient of friction between the bodies and the table is $0.15$. $A$ force of $200 \, N$ is applied horizontally to $A$. What are $(a)$ the reaction of the partition $(b)$ the action-reaction forces between $A$ and $B$? What happens when the wall is removed? Does the answer to $(b)$ change,when the bodies are in motion? Ignore the difference between $\mu_{s}$ and $\mu_{k}$.

$A$ cold soft drink is kept on a balance. When the cap is opened,the weight reading on the balance:

For the given system,find the value of $\theta_2$.