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 $(\mu = 0)$.

The maximum tension a rope can withstand is $60 \,kg$-wt. The ratio of maximum acceleration with which two boys of masses $20 \,kg$ and $30 \,kg$ can climb up the rope at the same time is

$A$ car of mass $1000\,kg$ is moving at a speed of $30\,m/s.$ Brakes are applied to bring the car to rest. If the net retarding force is $5000\,N,$ the car comes to stop after travelling $d\,m$ in $t\,s.$ Then

$A$ rod of length $L$ and mass $M$ is acted on by two unequal forces $F_1$ and $F_2$ $(F_2 < F_1)$ as shown in the figure. The tension in the rod at a distance $y$ from the end $A$ is given by:

$A$ 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 $g = 10\,m/s^2$)

$A$ chain is lying on an absolutely smooth table,with half of it hanging over the edge of the table as shown in figure $(a)$. The time it takes to slip off the table is affected if two equal weights are attached,one to each end as shown in figure $(b)$.
$t_a$ : time taken to slip in situation $(a)$
$t_b$ : time taken to slip in situation $(b)$