Two masses of $5\, kg$ and $10\, kg$ are connected to a pulley as shown. What will be the acceleration of the system if the pulley is set free? ($g =$ acceleration due to gravity)

$A$ particle of small mass $m$ is joined to a very heavy body of mass $M$ by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is

Three blocks of masses $m_1=4 \, kg$, $m_2=2 \, kg$, and $m_3=4 \, kg$ are connected with ideal strings passing over a smooth, massless pulley as shown in the figure. The acceleration of the blocks will be ......... $m/s^2$ $(g=10 \, m/s^2)$.

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:

The ends of a rope are held by two men who pull on it with equal and opposite forces of magnitude $F$ each. Then the tension in the rope is

In the system shown in the figure,the acceleration of the $1\,kg$ mass and the tension in the string connecting between $A$ and $B$ is