$A$ 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 $g = 10\, \text{m/s}^2$]

Two blocks,each of mass $M$,are initially at rest on frictionless surfaces as shown in the figure. If the pulleys are light and frictionless,and the block of mass $M$ on the incline is allowed to move down,then the tension in the string will be$-$

An elevator weighing $6000\,kg$ is pulled upward by a cable with an acceleration of $5\,ms^{-2}$. Taking $g$ to be $10\,ms^{-2}$,the tension in the cable is ............ $N$.

Three blocks of different masses connected with inextensible strings are pulled by a force $F$ on a frictionless surface as shown in the figure. The ratio of tensions $T_1$ to $T_2$ is

The mass of the lift is $200 \ kg$. When it ascends with an acceleration of $4 \ m/s^2$,the tension in the cable supporting the lift will be [Given: Acceleration due to gravity $g = 10 \ m/s^2$]. (in $N$)

$A$ 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).