If $m_1 = 4m_2$,and the acceleration of $m_1$ is $a$,then find $a$.

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. $A$ force $F$ applied on the upper string produces an acceleration of $2\,m/s^2$ in the upward direction in both the blocks. If $T$ and $T'$ are the tensions in the two parts of the string,then $T$ and $T'$ are:

$A$ 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

In the figure given below,with what acceleration will the block of mass $m$ move? (Pulley and strings are massless and frictionless)

To paint the side of a building,a painter normally hoists himself up by pulling on the rope $A$ as shown in the figure. The painter and platform together weigh $200 \, N$. The rope $B$ can withstand a maximum tension of $300 \, N$. Then:

$A$ monkey of mass $50\,kg$ climbs on a rope which can withstand the tension $(T)$ of $350\,N$. If the monkey initially climbs down with an acceleration of $4\,m/s^2$ and then climbs up with an acceleration of $5\,m/s^2$,choose the correct option $(g = 10\,m/s^2)$.