A uniform rod \(AB\) 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

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Correct Answer

(A) \(m,\frac{1}{x}\)

Step-by-step Solution

Detailed explanation

Balancing torque w.r.t point of suspension

\(\begin{array}{l}
mg\,x\, = Mg\left( {\frac{{.\ell }}{2} - x} \right)\\
\Rightarrow mx = M\frac{\ell }{2} - Mx\\
m = \left( {M\frac{\ell }{2}} \right)\frac{1}{x} - M\\
y = \alpha \frac{1}{x} - C,\,\,\,\,\,\,\,\,\, straight\,\, line\,\, equation.
\end{array}\)

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