A trolley of mass $5 \mathrm{kg}$ on a horizontal smooth surface is pulled by a load of mass $2 \mathrm{kg}$ by means of uniform rope $ABC$ of length $2 \mathrm{m}$ and mass $1 \mathrm{kg}$. As the load falls from $BC=0$ to $BC=2 \mathrm{m}$. its acceleration in $\mathrm{m} {\mathrm{s}}^{-2}$ changes

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 $\left[\sin 15°=0.26\right]$