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

Answer 1

Answer: (B)

Let length of rod $=l$, mass of rod$=M$.

At equilibrium, we have
$m\times x=M\times \left(\frac{l}{2}-x\right)=\frac{Ml}{2}-Mx$
On rearranging, we get
$m=\frac{ml}{2}\times \frac{1}{x}-M$
Now, comparing with equation of straight line: $y=mx+c$,
we see that the variables that give a straight line are $m,\frac{1}{x}$.