Question

Two blocks of masses $2\text{kg}$ and $4\text{kg}$ are arranged as shown in figure. Then, find the maximum value of force $F$, for which both blocks will move together.

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

Answer 1

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

For maximum value of force $F$, let two blocks move together with acceleration $a$.
First take two blocks as system:

The acceleration of the system will be, $a=\frac{F}{2+4}=\frac{F}{6}{\text{m/s}}^2$

Now from FBD of $2\text{kg}$ block:

The maximum frictional force will act on block, to avoid slipping on the surface.

$\therefore f_{max}=ma$
$\Rightarrow f_{max}=2\times \frac{F}{6}$
${\mu }_s\times mg=\frac{F}{3}$
$\therefore F=3\times 0.5\times 20=30\text{N}$

Hence option B is the correct answer.