Four blocks are connected as shown in the figure on a horizontal frictionless surface. If $m_1 = m_2 = m_3 = m_4 = m$,then the ratio $T_3 / T_4$ will be:

$A$ block of mass $M$ is kept on a platform which starts accelerating upwards from rest with a constant acceleration $a$. During the time interval $T$,the work done by the contact force on mass $M$ is

Two masses of $5 \,kg$ and $3 \,kg$ are suspended with the help of massless inextensible strings as shown in the figure below. When the whole system is moving upwards with an acceleration of $2 \,m/s^2$, the value of $T_1$ is (use $g = 9.8 \,m/s^2$): (in $\,N$)

Two blocks of $7\,kg$ and $5\,kg$ are connected by a heavy rope of mass $4\,kg$. An upward force of $200\,N$ is applied as shown in the diagram. The tension at the top of the heavy rope at point $P$ is ....... $N$ $(g = 10\,m/s^2)$.

$A$ uniform rope of mass $1.0\, kg$ is connected to a box of mass $2.0\, kg$,which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force of $6\, N$. Find the tension at the midpoint of the rope in $N$.

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The maximum velocity of the block during the subsequent motion of the system after the release of the ball is