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## QuestionPhysicsClass 11

A straight rod of length L has one of its end at the origin and the other at $${X}={L}$$. If the mass per unit length of the rod is given by $${A}{x}$$ where A is constant, where is its centre of mass?

$${x}_{{{C}{M}}}=\frac{{{\int_{{0}}^{{L}}}{x}{d}{m}}}{{{\int_{{0}}^{{L}}}{d}{m}}}=\frac{{{\int_{{0}}^{{L}}}{\left({X}\right)}{\left({A}{x}{\left.{d}{x}\right.}\right)}}}{{{\int_{{0}}^{{L}}}{\left({A}{x}{\left.{d}{x}\right.}\right)}}}=\frac{{2}}{{3}}{L}$$