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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 mLet 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=∫xdm∫dm xcom=∫105x(ML)dx∫105MLdx=∫105xdx∫105dx =15(x22)105 =15(102−522) =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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