A uniform $\operatorname{rod} A B$ is suspended from a point $X$, at a variable distance from $x$ from $A$,…
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:
$m, \frac{1}{x}$
$m, \frac{1}{x^2}$
$m, x$
$m, x^2$
Solution
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
