$A$ string tied to a roof can bear a maximum tension of $50 \,kg$ wt. The minimum acceleration with which a man of $98 \,kg$ can descend is ...... $m/s^2$ [Take $g = 9.8 \,m/s^2$].

With what minimum acceleration can a fireman slide down a rope if the breaking strength of the rope is $\frac{2}{3}$ of his weight?

Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in the figure. Calculate $T_1$ and $T_2$ when the whole system is moving upwards with an acceleration $a = 2\, m/s^2$ (use $g = 9.8\, m/s^2$).

$A$ force $F = 10t$ acts on a block of mass $m = 10 \, kg$ as shown in the figure. The coefficient of friction is $\mu = 0.4$. Find the time $t$ when the block loses contact with the surface.

$A$ 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 $N$.

$A$ block of mass $1 \, kg$ is suspended by a string of mass $1 \, kg$ and length $1 \, m$ as shown in the figure. Taking $g = 10 \, m/s^2$,calculate the force exerted by the support on the string. (in $, N$)