Question

In the arrangement shown in figure, wedge of mass $M$ moves towards left with an acceleration $a$. All surfaces are smooth. The acceleration of mass $m$ relative to wedge is :

• A. $\frac{a}{2}+\frac{\sqrt{3}}{2}g$
• B. $\frac{2Ma}{2}$
• C. $\frac{2(M+m)a}{m}$
• D. $\frac{(M+m)a}{m}$

Answer 1

The correct option is A $\frac{a}{2}+\frac{\sqrt{3}}{2}g$

Ref. image I Let us apply a pseudo force on block m towards right side.

$F_{pseudo}=ma$

Ref. image II acceleration relative to wedge $=g\sin \left({60}^{\circ }\right)+a\cos \left({60}^{\circ }\right)$

$=\frac{a}{2}+\frac{\sqrt{3}}{2}g$

Therefore option A is correct.