Question

Find the accelerations of the blocks $A$ and $B$ for the figure shown, if the system is initially at rest. Take $g=10{\text{m/s}}^2$.

• A. $\frac{4}{3}{\text{m/s}}^2$, zero
• B. zero, $\frac{5}{3}{\text{m/s}}^2$
• C. $3{\text{m/s}}^2,3{\text{m/s}}^2$
• D. $3{\text{m/s}}^2$, zero

Answer 1

The correct option is D $3{\text{m/s}}^2$, zero

The FBDs of the blocks are as shown.
Given, force applied on the block $A$ is $F=50\text{N}$


We have from the FBDs of the blocks
$N_1=10g=100\text{N}$
$f_{1\text{max}}=0.2\times 100=20\text{N}$
$N_2=N_1+20g=100+200=300\text{N}$
$f_{2\text{max}}=\left(0.4\right)\left(300\right)=120\text{N}$

Since, $f_{\text{2 max}}>f_{\text{1 max}}$, block $B$ will be at rest.
$\Rightarrow$ acceleration of the block $B$ will be zero.

For block $A$: Since, $F>f_{\text{1 max}}$, it will accelerate and the friction will be kinetic in nature
$\therefore$ Kinetic friction acting on block $A$ is $f_k=\mu N_1=0.2\times 10g=20\text{N}$
So, acceleration of the block $A$ is given by,
$a_A=\frac{F-f_k}{m_A}=\frac{50-20}{10}=3{\text{m/s}}^2$