Question

Find the maximum value of the magnitude of force $F$ for which the system will move together. Take $g=10{\text{m/s}}^2$.

• A. $20\text{N}$
• B. $30\text{N}$
• C. $50\text{N}$
• D. $75\text{N}$

Answer 1

The correct option is D $75\text{N}$

The FBDs of the blocks are as shown.
Given, the system of blocks will move together.
From the FBDs we have
$N_1=10g=100N$
$N_2=20g+N_1=200+100=300N$
$f_{\text{max}}={\mu }_s{N}_1=0.5\times 100=50\text{N}$

Now, for the blocks to move together, friction force required to be acted on block $B$ is
$f_{\text{max}}=50\text{N}$
Hence, acceleration of the system is $a=a_B=\frac{f_{\text{max}}}{m_B}=\frac{50}{20}=2.5{\text{m/s}}^2$
$\therefore F=(m_A+m_B)a=30\times 2.5=75\text{N}$