Question

In the figure shown if friction co-efficient of block $1$ and $2$ with inclined plane is ${\mu }_1=0.5$ and ${\mu }_2=0.4$ respectively, then find out the correct statement.

• A. there is a non-zero contact force between two blocks.
• B. both blocks will move sepeartely
• C. both blocks will move together
• D. none of these

Answer 1

The correct option is B both blocks will move sepeartely

If we consider block $1$ and $2$ independently,
The acceleration would be,
For block $\left(1\right)$
$a_1=g\sin \theta -{\mu }_{1}g\cos \theta a_1=g[\frac{\sqrt{3}}{2}-\frac{1}{2}\times \frac{1}{2}]=\frac{g[2\sqrt{3}-1]}{4}$
For block $\left(2\right)$
$a_2=g\sin \theta -{\mu }_{2}g\cos \theta a_2=g[\frac{\sqrt{3}}{2}-\frac{2}{5}\times \frac{1}{2}]=\frac{g}{10}[5\sqrt{3}-2]$
Since $a_2>a_1$, thus both blocks will move separately.