Question 130 of 280

A uniform rod $AB$ is suspended from a point $X$, at a variable distance $x$ from $A$, as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$. A set of $(m,x)$ value is recorded. The appropriate variables that give a straight line, when plotted, are:

A$m,{x}^{2}$B$m,\dfrac{1}{{x}^{2}}$C$m,\dfrac{1}{x}$D$m,x$

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Answer: (C) $m,\dfrac{1}{x}$

Net torque about suspension is zero,
$\Rightarrow mgx=Mg\left(\dfrac{l}{2}-x\right)$$\Rightarrow mx=M\dfrac{l}{2}-Mx$
$\Rightarrow m=\left(M\dfrac{l}{2}\right)\dfrac{1}{x}-M$$\Rightarrow y=\alpha \dfrac{1}{x}-C$, where,
$y=m,a=M\dfrac{l}{2}$ and $C=M$
it is the equation of straight line with variable $m$ and $\dfrac{1}{x}$.