If a ship of mass $4 \times 10^{7} \,kg$ initially at rest is pulled by a force of $5 \times 10^{4} \,N$ through a distance of $4 \,m$, then the speed of the ship will be (resistance due to water is negligible). (in $\,ms^{-1}$)

$A$ block of mass $M$ is placed on a horizontal surface and 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 the surface between $M$ and $m_0$ has a coefficient of friction $\mu$,find the tension in the string,assuming the system moves together.

The mass of a lift is $2000 \, kg$. When the tension in the supporting cable is $28000 \, N$,then its acceleration is:

On a smooth plane surface,two blocks $A$ and $B$ are accelerated by applying a force of $15 \, N$ on block $A$. If the mass of block $B$ is twice that of block $A$,the force on block $B$ is ........... $N$.

$A$ man slides down a light rope whose breaking strength is $\eta$ times the weight of the man $(\eta < 1)$. What is the maximum acceleration of the man so that the rope does not break?

Three blocks $A, B$ and $C$ weighing $1 \, kg, 8 \, kg$ and $27 \, kg$ respectively are connected as shown in the figure with an inextensible string and are moving on a smooth surface. If ${T_3} = 36 \, N$,then find the value of ${T_2}$ in $N$.