Question

In the system shown, the acceleration of the wedge of mass $5$M is?(there is no friction anywhere)

• A. Zero
• B. $g/2$
• C. $g/3$
• D. $g/4$

Answer 1

The correct option is A Zero

Let $a^{\prime }$ be the acceleration towards left.

From the Diagram,

$T-M{a}^{\prime }=Ma-----\left(1\right)$

$2M{a}^{\prime }cos{60}^0+2Mgsin{60}^0-T=2Ma-----\left(2\right)$

$=>M{a}^{\prime }+\sqrt{3}Mg-M{a}^{\prime }=3Ma=>a=\frac{g}{\sqrt{3}}$

Now, acceleration for the block 5,

$5M{a}^{\prime }+M(a+a^{\prime })=2M[acos{60}^0-a^{\prime }]$

$6M{a}^{\prime }+Ma=-2M{a}^{\prime }+Ma$

$a^{\prime }=0$