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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: m, 1/x; m, 1/x²; m, x; m, x²

m,1x2

m,x2

m,1x

m,x

Solution:

Let, 'l' and 'M' be the length and mass of rod.
for equilibrium, taking moment about X, we get
m × x = M × (l/2 - x)
this can be written as,
m = (M l/2) (1/x) - M
comparing with straight line equation, y = mx + c
we can say that, m ∝ 1/x