Question

Two blocks $A$ and $B$ of equal mass $m$ are connected through a massless string and arranged as shown in figure. Friction is absent everywhere. When the system is released from rest.

• A. tension in string is $\frac{mg}{2}$
• B. tension in string is $\frac{mg}{4}$
• C. acceleration of $A$ is $\frac{g}{2}$
• D. acceleration in the string is $\frac{3g}{4}$

Answer 1

The correct option is B tension in string is $\frac{mg}{4}$

$A$ & $B$ have equal mass $=m$

Given friction is absent every where

Now making FBD except fixed wedge

Let the system move with acceleration a after releasing (Ref. image 1)

Now

For $A$ (Ref. image 2)

$T+mg\sin {30}^o=ma$ ...(ii)

For $B$

$Mg-T=ma$ ...(i)

From (i) & (ii)

$mg-T=T+mg\sin {30}^o$

$2T=mg-\frac{mg}{2}$

$T=\frac{mg}{4}$

From (1)

$mg-T=ma$

$mg-\frac{mg}{4}=ma$

$\Rightarrow a=\frac{3a}{4}$

Hence tension in string is $\frac{mg}{4}$

Option B