$A$ force $F = 10t$ acts on a block of mass $m = 10 \, kg$ as shown in the figure. The coefficient of friction is $\mu = 0.4$. Find the time $t$ when the block loses contact with the surface.

In the diagram shown,the normal reaction force between the $2\,kg$ and $1\,kg$ blocks is (Consider the surface to be smooth) $.........N$ (Given $g = 10\,ms^{-2}$)

With what minimum acceleration can a fireman slide down a rope if the breaking strength of the rope is $\frac{2}{3}$ of his weight?

$A$ body of mass $2 \, kg$ moves under a force of $(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) \, N$. It starts from rest and was at the origin initially. After $4 \, s$,its new coordinates are $(8, b, 20)$. The value of $b$ is ........ . (Round off to the Nearest Integer)

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

$A$ constant horizontal force $\overrightarrow{F}$ of magnitude $10 \,N$ is applied to a block $A$ and this produces an acceleration of magnitude $20 \,m/s^2$. If this block $A$ is then kept against another block $B$ of mass $1.5 \,kg$ as shown in the figure and a force $F^{\prime}$ of $20 \,N$ is applied,find the force on the block $B$. Neglect friction. (in $N$)