A thin rod of length ' \( L \) ' lying along the \( x \)-axis with its ends at \( x=0 \) and \( ...

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A thin rod of length ' \( L \) ' lying along the \( x \)-axis with its ends at \( x=0 \) and \( x=L \). Its linear density (mass/length) varies with \( x \) as \( k\left(\frac{x}{L}\right)^{n} \), where \( n \) can be zero or any positive number. If the position \( x_{c m} \) of the centre of mass of the rod is plotted against ' \( n \) ', which of the following graphs best approximates the dependence of \( x_{c m} \) on \( n \)
[AIEEE 2008]
(a) \( L / 2 \)
(c)
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