Question 132 of 280

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

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

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Answer: (A) $m, \frac{1}{x}$

Balancing torque w.r.t. point of suspension
$$\begin{aligned} &m g x=M g\left(\frac{\ell}{2}-x\right) \\ &\Rightarrow m x=M \frac{\ell}{2}-M x \\ &m=\left(M \frac{\ell}{2}\right) \frac{1}{x}-M \end{aligned}$$


$y=\alpha \frac{1}{x}-C \quad$ Straight line equation.