Three equal weights $A, B$ and $C$ of mass $2\, kg$ each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string connecting weights $B$ and $C$ is ........... $N$.

$A$ 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?

For the system shown in the figure,$m_1 > m_2 > m_3 > m_4$. Initially,the system is at rest in equilibrium. If the string joining $m_4$ and the ground is cut,then just after the string is cut:
Statement $I$: $m_1$,$m_2$,and $m_3$ remain stationary.
Statement $II$: The value of acceleration of all the $4$ blocks can be determined.
Statement $III$: Only $m_4$ remains stationary.
Statement $IV$: Only $m_4$ accelerates.
Statement $V$: All the four blocks remain stationary.
Now,choose the correct option.

$A$ hanging mass $M$ is connected to a four times larger mass $(4M)$ by using a string-pulley arrangement as shown in the figure. The larger mass is placed on a horizontal ice slab and is being pulled by a $2Mg$ force. In this situation,the tension in the string is $\frac{x}{5}Mg$. Find the value of $x$. Neglect the mass of the string and the friction between the block (larger mass) and the ice slab. (Given $g$ = acceleration due to gravity)

In the arrangement shown in the figure,the pulleys are massless and frictionless,and the threads are inextensible. The block of mass $m_1$ will remain at rest,if

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 $g = 10\, ms^{-2}$)