$A$ 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 $g = 9.8 \,m/s^2$].

$A$ 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 $18.5 \ kg$ kept on a smooth horizontal surface is pulled by a rope of $3 \ m$ length by a horizontal force of $40 \ N$ applied to the other end of the rope. If the linear density of the rope is $0.5 \ kg \ m^{-1}$ and initially the block is at rest,the time in which the block moves a distance of $9 \ m$ is: (in $s$)

Two blocks of masses $6 \ kg$ and $4 \ kg$ are placed in contact with each other on a smooth surface as shown. If a force of $5 \ N$ is applied on the heavier block,the force on the lighter block is (in $N$)

$A$ car of mass $1250 \ kg$ is moving at $30 \ m/s$. Its engine delivers $30 \ kW$ while the resistive force due to the surface is $750 \ N$. What is the maximum acceleration that can be given to the car in $m/s^2$?

Two spheres $P$ and $Q$ of equal masses $m$ are attached to a string of total length $2\, m$ as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular velocity $\omega$. The distance $OP = 1\, m$ and $PQ = 1\, m$. What is the value of the ratio $\left( \frac{\text{Tension in the string between } P \text{ and } Q}{\text{Tension in the string between } O \text{ and } P} \right)?$