Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface as shown in the figure. The tension in the string will be

$A$ steel block of $10\, \text{kg}$ rests on a horizontal floor. When three iron cylinders,each of mass $20\, \text{kg}$,are placed on it as shown,the entire system (block + cylinders) moves downward with an acceleration of $0.2\, \text{m/s}^2$. The normal reaction $R$ exerted by the floor is ..... $\text{N}$. [Take $g = 10\, \text{m/s}^2$]

Three solids of masses $m_1, m_2$ and $m_3$ are connected with weightless strings in succession and are placed on a frictionless table. If the mass $m_3$ is dragged with a force $T$,the tension in the string between $m_2$ and $m_3$ is

If the breaking strength of a rope is $\frac{4}{3}$ times the weight of a person,then the maximum acceleration with which the person can safely climb up the rope is ($g$ = acceleration due to gravity).

$A$ block $P$ of mass $M_P$ is in contact with another block $Q$ of mass $M_Q$ as shown in the figure and they are placed on a smooth floor. Find the force on block $Q$.

$A$ monkey of mass $40 \, kg$ climbs on a rope which can stand a maximum tension of $600 \, N$. In which of the following cases will the rope break: the monkey
$(a)$ climbs up with an acceleration of $6 \, m \, s^{-2}$
$(b)$ climbs down with an acceleration of $4 \, m \, s^{-2}$
$(c)$ climbs up with a uniform speed of $5 \, m \, s^{-1}$
$(d)$ falls down the rope nearly freely under gravity? (Ignore the mass of the rope).