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Question

A uniform rod of length 5 m is placed along x - axis as shown in the figure. The position of centre of mass of the rod from the origin is


A
2.5 m
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B
5 m
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C
7.5 m
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D
10 m
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Solution

The correct option is C 7.5 m
Let the mass of uniform rod be M
Mass per unit length of the rod =(ML) is constant since the rod is uniform.

Let dm be the mass of an element of length dx at a distance x from origin
dm=(ML)dx=(M5)dx

Position of centre of mass, xcom=xdmdm
xcom=105x(ML)dx105MLdx=105xdx105dx
=15(x22)105
=15(102522)
=7510=7.5 m

Alternate:
As from symmetry we can say that the COM of the rod will lie at L2, since rod is uniform
So, from origin COM will be at 5+52=7.5 m

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