Two masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in the figure. A force of 200 N acts on the 20 kg mass. At the instant shown the 10 kg mass has an acceleration 4 m/s² rightwards. What is the acceleration of 20 kg mass ?

                            

The pulley arrangements shown in the figure are identical, the mass of the rope being negligible. In case (a) mass m is lifted by attaching a mass of 2m to the other end of the rope. In case (b) the mass m is lifted by pulling the other end of the rope with a constant downward force F = 2mg, where g is the acceleration due to gravity. The acceleration of mass m in case (a) is :-

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