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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 :

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a

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

b

$m, \frac{1}{x^{2}}$

c

$m, x^{2}$

d

m, x

answer is B.

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Detailed Solution

Let the rod's length and mass be l and M, respectively.
If we choose X as the point of equilibrium, we obtain

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

can be written as,

$m = (\frac{M l}{2}) \frac{1}{x} - M$

comparing the equation with y=mx+c

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

Hence the correct answer is $m, \frac{1}{x} .$

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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 :