Question

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:

• A. $m,\frac{1}{x}$
• B. $m,\frac{1}{x^2}$
• C. $m,x$
• D. $m,x^2$

Answer 1

Answer: (A)

Let, 'l' and 'M' be the length and mass of rod.

for equilibrium, taking moment about X, we get

$m\times x=M\times (\frac{l}{2}-x)$

this can be written as,

$m=\left(\frac{Ml}{2}\right)\frac{1}{x}-M$

comparing with straight line equation,

y = mx + c

we can say that,

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