In the arrangement shown,the mass $m$ will ascend with an acceleration (Pulley and rope are massless).

$A$ 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.

$A$ man of mass $60 \ kg$ is standing on a platform of mass $40 \ kg$ as shown in the figure. What force should the man apply on the rope so that he accelerates upward with the platform with an acceleration of $2 \ m/s^2$ (in $N$)? (Take $g = 10 \ m/s^2$)

Two masses $M$ and $M/2$ are joined together by means of a light inextensible string passing over a frictionless pulley as shown in the figure. When the bigger mass is released,the smaller one will ascend with an acceleration of

Two weights $2 \,N$ and $3 \,N$ are suspended from the ends of an inextensible string passing over a fixed frictionless pulley. If the pulley is pulled up with an acceleration equal to the acceleration due to gravity $(g)$, then the tension in the string is: (in $\,N$)

Two blocks of masses $m_1$ and $m_2$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration $a_0 = g$,then the tension in the string will be