In the arrangement shown in figure, pulley is smooth and massless and all the strings are light. Let $F_1$ be the force exerted on the pulley in case $\left(\mathrm{i}\right)$ and $F_2$ the force in case $\left(\mathrm{ii}\right)$. Then

In the figure, the blocks $A$, $B$ and $C$ each of mass $m$ have acceleration $a_1$, $a_2$ and $a_3$, respectively. $F_1$ and $F_2$ are external forces of magnitudes $2mg$ and $mg$, respectively. Then

In the arrangement shown in figure $m_1=1 \mathrm{kg}, m_2=2 \mathrm{kg}$. Pulleys are massless and string are light. For what value of $M$ the mass $m_1$ moves with constant velocity (Neglect friction)

A trolley is being pulled up an incline plane a man sitting on it (as shown in figure). He applies a force of $250 \mathrm{N}$. If the combined mass of the man and trolley is $100 \mathrm{kg}$, the acceleration of the trolley will be $\left[\sin 15°=0.26\right]$

A man think about $4$ arrangements as shown to raise two small bricks each having mass $m$. Which of the arrangement would take minimum time?

In the arrangement shown in the figure neglect the masses of the pulley and string and also friction. The accelerations of blocks $A$ and $B$ are

A block is placed on an inclined plane moving towards right horizontally with an acceleration $a_0=g$. The length of the plane $AC=1 \mathrm{m}$. Friction is absent everywhere. The time taken by the block to reach from $C$ to $A$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In the arrangement shown in figure pulley $A$ and $B$ are massless and the thread is in extensible. Mass of pulley $C$ is equal to $m$. If friction in all the pulleys is negligible, then