A) \[\frac{3\,(2+b)}{4\,(3+b)}\]
B) \[\frac{4\,(2+b)}{3\,(3+b)}\]
C) \[\frac{3\,(2+b)}{4\,(2+b)}\]
D) \[\frac{4\,(3+b)}{3\,(2+b)}\]
E) \[\frac{2\,(3+b)}{3\,(6+b)}\]
Correct Answer: A
Solution :
Here \[\rho (x)=a\,(1+b{{x}^{2}})\] When \[b\to 0\,(x)=a\]constant i.e. density of rod of length 1m is constant. In that event centre of mass of rod would lie at 0.5m (i.e. at the cutre of rod). When are try \[b\to 0\] in all the four given option, we find choice alone given \[x=\frac{3\,(2+b)}{4\,(3+b)}\] \[=\frac{6}{12}=0.5\]You need to login to perform this action.
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