Question

In the given figure, masses of $A$ and $B$ are $5\text{kg}$ and $10\text{kg}$ respectively. Coefficient of friction between blocks is 0.2. If the lower block is pulled rightwards with a constant force, $F=50\text{N}$, time elapsed before block $A$ falls off block $B$ is: (There is no friction between block $B$ and surface) and neglect the size of $A$)

• A. $2s$
• B. $\frac{3}{\sqrt{2}}s$
• C. $\frac{2}{\sqrt{3}}s$
• D. $\sqrt{\frac{3}{2}}s$

Answer 1

The correct option is B $\frac{3}{\sqrt{2}}s$

FBD of $B$

$50-f_k=10a$
$50-\left(0.2\right)\left(50\right)=10a$
$\Rightarrow 10a=40$
$a=4{\text{ms}}^{-2}$
FBD of $A$ (rest frame of $B$)
$ma-f_k=m{a}_1$
$5\left(4\right)-10=5a_1$
$\Rightarrow a_1=2{\text{ms}}^{-2}$
Block $A$ has to travel a distance of $4.5\text{m}$ w.r.t $B$, before falling off.
$l=0\left(t\right)+\frac{1}{2}\left(a_1\right)t^2$
$4.5=\frac{1}{2}\left(2\right)t^2\Rightarrow t=\sqrt{\frac{9}{2}}=\frac{3}{\sqrt{2}}$