Question

Three blocks $A,B,$ and $C$ are suspended as shown in figure. Mass of block $A$ and $B$ is $m$ each. If the system is in equilibrium and mass of $C$ is $M$, then

• A. $M\ge 2m$
• B. $M=2m$
• C. $M\le 2m$
• D. None of these

Answer 1

The correct option is C $M\le 2m$


From FBD of $C$,
$2T\cos \theta =Mg$
and from FBD of $B$,
$T=mg$
$\therefore$ $2mg\cos \theta =Mg$
$\Rightarrow \cos \theta =\frac{Mg}{2mg}=\frac{M}{2m}$

If $0^{\circ }\le \theta \le {90}^{\circ }$, then $1\ge \cos \theta \ge 0$
Hence, $1\ge \frac{M}{2m}\ge 0$
$\therefore M\le 2m$
Option C is correct.