Three masses of $1 \mathrm{kg}$, $6 \mathrm{kg}$ and $3 \mathrm{kg}$ are connected to each other with threads and are placed on a table as shown in the figure. What is the acceleration with which the system is moving? (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The surface is frictionless, the ratio of $T_1$ and $T_2$ is

Two blocks of masses $6 \mathrm{kg}$ and $4 \mathrm{kg}$ connected by a rope of mass $2 \mathrm{kg}$ are resting on a frictionless floor as shown in the following figure. If a constant force of $60 \mathrm{N}$ is applied to $6 \mathrm{kg}$ block, then the tension in the rope at points $A$, $B$ and $C$ are, respectively, given by

Two masses of $10 \mathrm{kg}\text{ and} 5 \mathrm{kg}$ are suspended from a fixed support as shown in figure. The system is pulled down with a force of $150 \mathrm{N}$ attached to the lower mass. The string attached to the support breaks and the system accelerates downwards. If the downward force continues to act, what is the acceleration of the system ?

In the figure, mass $M=10 \mathrm{g}$ is placed on an inclined plane. In order to keep it at rest, the value of mass $m$ will b

A block is dragged on a smooth plane with the help of a rope which moves with a velocity $v$ as shown in figure. The horizontal velocity of the block is