Question

What is the acceleration (in ${\text{m/s}}^2)$ of the block of mass $m$ relative to the wedge of mass $M$ for the figure shown? Assume all surfaces to be smooth. Take $g=10{\text{m/s}}^2$.

• A. $\frac{2}{\sqrt{3}}$
• B. $\frac{10-3\sqrt{3}}{2}$
• C. $4\sqrt{3}$
• D. $\frac{10\sqrt{3}-3}{2}$

Answer 1

The correct option is B $\frac{10-3\sqrt{3}}{2}$

Using concept of pseudo force in the frame of mass $M$

Along the plane
$mg\sin \theta -ma\cos \theta =m{a}_r$
$\Rightarrow a_r=g\sin \theta -a\cos \theta$
$\because$ $\theta ={30}^{\circ }$
$\Rightarrow a_r=5-\frac{3\sqrt{3}}{2}\Rightarrow a_r=\frac{10-3\sqrt{3}}{2}{\text{m/s}}^2$