$A$ 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 $m/s^2$?

Three blocks of masses $2 \, kg, 3 \, kg$ and $5 \, kg$ are connected to each other with light strings and are placed on a frictionless surface as shown in the figure. The system is pulled by a force $F = 10 \, N$. Find the tension $T_1$ in the string between the $2 \, kg$ and $3 \, kg$ blocks. (in $, N$)

Two blocks of masses $5\, kg$ and $4\, kg$ are in contact with each other on a frictionless table. When a horizontal force of $9\, N$ is applied to the block of mass $5\, kg$,then the value of the force of contact between the two blocks is ........ $N$.

The mass of a lift is $500\, kg$. When it ascends with an acceleration of $2\, m/s^2$,the tension in the cable will be........... $N$ $[g = 10\, m/s^2]$

$A$ block of mass $M$ is placed on a horizontal surface and it is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If $\mu < \mu_{min}$ (the minimum friction required to keep the block $m$ stationary),then the downward acceleration of $m$ is:

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