A) \[\frac{L}{3}\]
B) \[\frac{L}{2}\]
C) \[\frac{2L}{3}\]
D) \[\frac{3L}{4}\]
Correct Answer: B
Solution :
Let the mass of an element of length \[dx\]of rod located at distance \[x\]away from left end is\[\frac{M}{L}dx.\]The \[x-\]coordinate of the centre of mass is given by \[{{x}_{CM}}=\frac{1}{M}\int_{{}}^{{}}{x\,dm=0}\] \[=\frac{1}{M}\int_{0}^{L}{x\left( \frac{M}{L}dx \right)}\] \[=\left[ \frac{1}{L}\frac{{{x}^{2}}}{2} \right]_{0}^{L}=\frac{L}{2}\] The \[y-\]coordinate is \[{{Y}_{CM}}=\frac{1}{M}\int_{{}}^{{}}{y\,dm}=0\] and similarly, \[{{z}_{CM}}=0\] The centre of the mass is at\[\left( \frac{L}{2},0,0 \right)\] or at the middle point of the rod, i.e., at\[\frac{L}{2}.\]You need to login to perform this action.
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