A) a = b
B) a = 2b
C) 2a = b
D) 3a = 2b
Correct Answer: C
Solution :
\[{{X}_{COM}}=\frac{\int\limits_{0}^{L}{\left( \mu dx \right)x}}{\int\limits_{0}^{L}{\mu dx}}\] \[\frac{7}{12}L=\frac{\int\limits_{0}^{L}{\left( ax+\frac{b{{x}^{2}}}{L} \right)dx}}{\int\limits_{0}^{L}{\left( a+\frac{bx}{L} \right)dx}}\] \[\frac{7}{12}L=\frac{\left( \frac{b{{L}^{3}}}{3L}+\frac{a{{L}^{2}}}{2} \right)}{\left( aL+\frac{bL}{2} \right)}\] \[\frac{7}{12}=\frac{\frac{a}{2}+\frac{b}{3}}{a+\frac{b}{2}}\] \[\therefore \]\[\] \[\therefore \,\,\,\,2a=b\]You need to login to perform this action.
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