Question

In the figure shown, find the acceleration (in $m/s^2$) of the blocks if the wedge is fixed. (String is massless and inextensible)

• A. $2g$
• B. $\frac{g}{3}$
• C. $\frac{g}{4}$
• D. $g$

Answer 1

The correct option is C $\frac{g}{4}$

The FBDs of the masses are as shown

Let the direction of the acceleration $a$ be as shown in the figure and tension in the string be $T$

So, from the FBDs we have
$T-4g.sin{30}^{\circ }=4a⟹T-2g=4a$........(i)
And, $4g-T=4a$.........(ii)
From eq (i) & (ii) we have,
$2g=8a⟹a=\frac{g}{4}$

Alternate:
Let the two blocks collectively form a system. So, the acceleration of the system is given by
$a=\frac{\text{Effective force}}{\text{Total mass}}$
Here, effective force on the system is given by
$4g-4gsin{30}^{\circ }=2g$
$\therefore a=\frac{4g-2g}{8}=\frac{g}{4}$