Question

In the figure shown, the static friction between all contact surfaces is $0.5$. What minimum force applied leftwards on block $1$ will move the system?

• A. $10\text{N}$
• B. $20\text{N}$
• C. $30\text{N}$
• D. $40\text{N}$

Answer 1

The correct option is C $30\text{N}$

FBD of block $1$ and $2$ :


At critical situation,

$F=f_1+f_2+T$ [ For block $1$ ]

$F={\mu }_s{N}_1+{\mu }_s{N}_2+T$

$F=0.5\times 2\times 10+0.5\times 3\times 10+T$

$F=25+T$ ........... $\left(1\right)$


$f_1=2T$ [ For block $2$ ]

$f_1={\mu }_s{N}_1=0.5\times 2\times 10=10\text{N}$

$\Rightarrow T=5\text{N}$ .........$\left(2\right)$

Substituting $\left(2\right)$ in $\left(1\right)$

$F=30\text{N}$

Hence, option (c) is the correct answer.

Why this question ? Key Concept: Due to string constraint both the block will be at the verge of slipping simultaneously