A uniform rod AB is suspended from a point X, at a variable distance… | JEE Main 2018 (15 Apr, Shift 1)

Q38JEE Main 2018 · 15 APR · SHIFT 1Medium

Torque, Couple & Equilibrium of Rigid Bodies

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 $(m, x)$ values is recorded. The appropriate variables that give a straight line, when plotted, are:

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Answer: (b)

Let the rod have mass $M$ and length $L$ ; its weight acts at $L/2$ from A.
Moments about X: $mg\,x = Mg\left(\frac{L}{2} - x\right)$
$m = \frac{ML}{2}\cdot\frac{1}{x} - M$ , a straight line between $m$ and $\frac{1}{x}$ .
So the answer is (b) $m, \frac{1}{x}$ .

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