Question

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

• A. $20.67{\text{m/s}}^2,3.6{\text{m/s}}^2$
• B. $3.6{\text{m/s}}^2,2.7{\text{m/s}}^2$
• C. $10{\text{m/s}}^2$, zero
• D. Zero, $10{\text{m/s}}^2$

Answer 1

The correct option is A $20.67{\text{m/s}}^2,3.6{\text{m/s}}^2$

The FBDs of the blocks are as shown

From the FBDs we have
$N_1=m_{A}g=1.5g=15\text{N}$
$N_2=N_1+2.5g=15+25=40\text{N}$
$f_{\text{max}}=\mu N_1=0.6\times 15=9\text{N}$

Assume that both the blocks will move together, then the common acceleration is given by,
$a_c=\frac{F}{m_A+m_B}=\frac{40}{1.5+2.5}=10{\text{m/s}}^2$

From the block $B$ we have required friction force $f$ to make blocks move together
$\Rightarrow f=m_B{a}_c=2.5\times 10=25\text{N}$
$\because f>f_{\text{max}}$, our assumption is wrong here.
So, they will slip over each other and move separately with different acceleration.
$\therefore a_A=\frac{40-f_{\text{max}}}{1.5}=\frac{40-9}{1.5}=20.67{\text{m/s}}^2$
and, $a_B=\frac{f_{\text{max}}}{2.5}=\frac{9}{2.5}=3.6{\text{m/s}}^2$