$A$ block of mass $M$ is lying on a horizontal frictionless surface. One end of a uniform rope of mass $M/2$ is fixed to the block, which is pulled in the horizontal direction by applying a force $F$ at the other end. The tension in the middle of the rope will be

For the given figure,find the value of $m$ (in $kg$) for which the blocks have an acceleration of $\frac{8}{13}g$. The block on the incline has a mass of $100 \, g = 0.1 \, kg$ and the hanging block on the left has a mass of $50 \, g = 0.05 \, kg$. The surface is frictionless $(\mu = 0)$.

$A$ monkey of mass $20\,kg$ is holding a vertical rope. The rope will not break when a mass of $25\,kg$ is suspended from it but will break if the mass exceeds $25\,kg$. What is the maximum acceleration with which the monkey can climb up along the rope in $m/s^2$? (Take $g = 10\,m/s^2$)

$A$ monkey of mass $40 \, kg$ climbs on a rope which can stand a maximum tension of $600 \, N$. In which of the following cases will the rope break: the monkey
$(a)$ climbs up with an acceleration of $6 \, m \, s^{-2}$
$(b)$ climbs down with an acceleration of $4 \, m \, s^{-2}$
$(c)$ climbs up with a uniform speed of $5 \, m \, s^{-1}$
$(d)$ falls down the rope nearly freely under gravity? (Ignore the mass of the rope).

Two blocks,each having mass $M$,rest on frictionless surfaces as shown in the figure. If the pulleys are light and frictionless,and $M$ on the incline is allowed to move down,then the tension in the string will be

Three blocks $A$,$B$,and $C$ of masses $5 \text{ kg}$,$3 \text{ kg}$,and $2 \text{ kg}$ respectively are pulled on a horizontal smooth surface by a force of $80 \text{ N}$ as shown in the figure. The tensions $T_1$ and $T_2$ in the strings are respectively: