Question

Find the maximum value of $F$ such that both the blocks move together. Take $g=10{\text{m/s}}^2$.

• A. $200\text{N}$
• B. $150\text{N}$
• C. $100\text{N}$
• D. $50\text{N}$

Answer 1

The correct option is B $150\text{N}$

As we know that, for maximum value of force $F$, the friction will be limiting.
Also, as per given condition, both the blocks are moving together.
We have FBDs of both the blocks as



We have
$N_1=10g=100N$
$N_2=N_1+20g=100+200=300N$
$f=f_{limiting}=f_{max}=\mu N_1=0.5\times 100=50N$

$\because$ the blocks moves together, the common acceleration is given by
$a_c=\frac{F}{m_A+m_B}=\frac{F}{10+20}=\frac{F}{30}{\text{m/s}}^2$

Now, from the FBD of block $B$ we have
$F-f=m_B{a}_c\Rightarrow F-50=20\times \frac{F}{30}$
$\Rightarrow (F-\frac{2F}{3})=50$
$\Rightarrow F=3\times 50=150N$