Two blocks are in contact on a frictionless table. One has mass $m$ and the other $2\,m$. $A$ force $F$ is applied on $2\,m$ as shown in the figure. Now,the same force $F$ is applied from the right on $m$. In the two cases respectively,what is the ratio of the contact force between the two blocks?

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 $N$)

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$-$

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 ........ $N$.

$A$ 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).

Two blocks of masses $7 \, kg$ and $5 \, kg$ are placed in contact with each other on a smooth surface. If a force of $6 \, N$ is applied on the heavier mass,the force on the lighter mass is ............ $N$.