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  4. 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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Q. 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 :Physics Question Image

JEE MainJEE Main 2018System of Particles and Rotational Motion

Solution:

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