Question

Find the acceleration of block $A$ and $B$? Take $g=10m/s^2$

• A. $a_A=1{\text{m/s}}^2,a_B=1{\text{m/s}}^2$
• B. $a_A=2{\text{m/s}}^2,a_B=2{\text{m/s}}^2$
• C. $a_A=2{\text{m/s}}^2,a_B=1{\text{m/s}}^2$
• D. $a_A=1{\text{m/s}}^2,a_B=2{\text{m/s}}^2$

Answer 1

The correct option is A $a_A=1{\text{m/s}}^2,a_B=1{\text{m/s}}^2$

External force $F=90N$ is given on lower block.
So, we have check whether they will slide together (or) not.

From FBDs of $A$ and $B$ we have
$f_{\text{1 max}}=\mu N=0.5\left(5g\right)=25\text{N}$
$f_{\text{2 max}}=\mu N=0.5\left(15g\right)=75\text{N}$
As, $90\text{N}>75\text{N}$
$\Rightarrow F_{\text{External}}$ > friction available$\left(f_{\text{2 max}}\right)$
Writing equation of motion for block $B$ (both slides together)
$90-75=(10+5)a$
$15=15a$
$a=1{\text{m/s}}^2$

Now, we have to check whether on block $A$ enough driving force is available to produce this common acceleration.
$\therefore F_{\text{required}}=m_{A}a=5\left(1\right)=5\text{N}$
Block $A$ is having the driving force $25\text{N}$
So, $F_{\text{Driving of}A}>F_{\text{required for}A}$
Hence, the both block will slide together with the common acceleration of $1{\text{m/s}}^2$.