Q 11-06-235JEE MainJEE Main 2018 (15 Apr, Shift 1)Medium
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:
Answer: (C) $m,\ \dfrac{1}{x}$
Let the rod have mass $M$ and length $L$; its weight acts at the midpoint, a distance $\left(\frac L2 - x\right)$ from $X$.
Taking moments about $X$ for the horizontal rod:
$$mg\,x = Mg\left(\frac{L}{2} - x\right)$$
$$m = \frac{ML}{2}\cdot\frac{1}{x} - M$$
So $m$ is a linear function of $\dfrac1x$: plotting $m$ against $\dfrac1x$ gives a straight line (slope $\dfrac{ML}{2}$, intercept $-M$).
Solution by Sreeraj P, M.Sc Physics