Three blocks of masses $4\,kg$,$6\,kg$ and $8\,kg$ are hanging over a fixed pulley as shown. The tension in the string connecting the $8\,kg$ and $4\,kg$ blocks is:

Three blocks of masses $m_1=4 \, kg$, $m_2=2 \, kg$, and $m_3=4 \, kg$ are connected with ideal strings passing over a smooth, massless pulley as shown in the figure. The acceleration of the blocks will be ......... $m/s^2$ $(g=10 \, m/s^2)$.

$A$ painter is applying force himself to raise him and the box with an acceleration of $5\, m/s^2$ by a massless rope and pulley arrangement as shown in the figure. The mass of the painter is $100\, kg$ and that of the box is $50\, kg$. If $g = 10\, m/s^2$,then:

Given $m_1 = 4m_2$. The acceleration of $m_1$ is $a$. The time taken for $m_1$ to reach the ground is ........ $\text{sec}$. (Assume the initial height is $0.2 \text{ m}$)

$A$ 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.

$A$ loop of light inextensible string passes over smooth small pulleys $A$ and $B$. Two masses $m$ and $M$ are attached to the points $O$ and $C$ respectively. The condition that $m$ and $M$ will cross each other (given $AB = 2l$ and $AC = BC = \eta l$) is: