A uniform rod AB is suspended from a point X, at a variable dista… - Vidyadip

MCQ

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

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

✓

Answer

Correct option: A.

$m,\frac{1}{x}$

a
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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