Question

A mass $M$ is hung with a light inextensible string as shown in the figure. Find the tension of the horizontal string.

• A. $\sqrt{2}Mg$
• B. $\sqrt{3}Mg$
• C. $2Mg$
• D. $3Mg$

Answer 1

Answer: (B)

As here is a load at $P$, so tension in $AP$ and $PB$ will be different as shown in figure. Let these tensions be $T_1$ and $T_2$, respectively.
For vertical equilibrium of $P$,

$T_2\cos 60^{\circ }=Mg$ ...(i)
i.e. $T_2=2Mg$
and for horizontal equilibrium of $P$,
$T_1=T_2\sin 60^{\circ }=T_2(\sqrt{3}/2)$ ...(ii)
Substituting the value of $T_2$ from Eq. (i), we get
$T_1=(2Mg)\times (\sqrt{3}/2)=\sqrt{3}Mg$