Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in the figure. The whole system is moving upwards with an acceleration of $2\, ms^{-2}$. The tensions $T_1$ and $T_2$ are respectively (Take $g = 10\, ms^{-2}$)

In the pulley system shown, the mass of the ball is $1.2$ times greater than the mass of the rod. The length of the rod is $50 \,cm$. The ball is set on the same level as the lower end of the rod and then released. What is the acceleration of the rod with which it comes down (in $\,m/s^2$)? Assume the pulleys and threads are massless and friction is neglected. (Use $g = 10 \,m/s^2$)

$A$ weight $W$ can be hung in any of the following four ways by a string of the same type. In which case is the string most likely to break?

$A$ bob of mass $m$ is hanging from a pulley inside a car by a string. The other end of the string is held by a person standing in the car. The car is moving with a constant horizontal acceleration '$a$' as shown in the figure. The other end of the string is pulled with a constant acceleration '$a$' vertically downward. The tension in the string is equal to-

$A$ 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

Two bodies of mass $3\, kg$ and $4\, kg$ are suspended at the ends of a massless string passing over a frictionless pulley. The acceleration of the system is ........ $m/s^2$ $(g = 9.8\, m/s^2)$.