Question

Find the acceleration of the two bodies ($A$ and $B$), if the system shown is initially at rest.
Take $g=10{\text{m/s}}^2$.

• A. $a_A=a_B=\frac{4}{3}{\text{m/s}}^2$
• B. $a_A=\frac{4}{3}{\text{m/s}}^2;a_B=0$
• C. $a_A=0;a_B=\frac{4}{3}{\text{m/s}}^2$
• D. $a_A=2{\text{m/s}}^2;a_B=4{\text{m/s}}^2$

Answer 1

The correct option is A $a_A=a_B=\frac{4}{3}{\text{m/s}}^2$

The FBDs of the blocks are as shown


$N_1=10g=100\text{N}$
$N_2=N_1+5g=100+50=150\text{N}$
$f_{\text{max}}=\mu N_1=0.5\times 100=50\text{N}$

Assuming that the two blocks move together, then the Common acceleration is
$a_c=\frac{F}{m_1+m_2}=\frac{20}{15}=\frac{4}{3}{\text{m/s}}^2$

From FBD of $B:$ Required frictional force $f$ to make them move together is
$f=m{a}_c=5\times \frac{4}{3}=\frac{20}{3}\text{N}$
Since, $\frac{20}{3}N<50N$
$\Rightarrow f<f_{\text{max}}$, it means our assumption was right, they will move together
Hence, $a_A=a_B=\frac{4}{3}{\text{m/s}}^2$