$A$ student calculates the acceleration of $m_1$ in the figure shown as $a_1 = \frac{(m_1 - m_2)g}{m_1 + m_2}$. Which assumption is not required to do this calculation?

An inextensible string passing over a smooth pulley connects two blocks of masses $m_1$ and $m_2$ $(m_2 > m_1)$ vertically. If the acceleration of the system is $(\frac{g}{n})$, then the ratio of masses $(\frac{m_2}{m_1})$ is

$A$ pulley fixed to the ceiling carries a string with blocks of mass $m$ and $3m$ attached to its ends. The masses of the string and pulley are negligible. When the system is released,what is the acceleration of its center of mass?

Two masses $M_{1}$ and $M_{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_{2}$ is twice that of $M_{1}$,the acceleration of the system is $a_{1}$. When the mass $M_{2}$ is thrice that of $M_{1}$,the acceleration of the system is $a_{2}$. The ratio $\frac{a_{1}}{a_{2}}$ will be:

If the system is in equilibrium,what should be the tension in the rope?

$A$ rope of length $5\,m$ is kept on a frictionless surface and a force of $5\,N$ is applied to one of its ends. Find the tension in the rope at $1\,m$ from this end.