question_answer

A thin rod of length ‘L’ is 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 \[{{x}_{CM}}\] of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of \[{{x}_{CM}}\] on n?                            [AIEEE 2008]

A)   

B)        

C)   

D)        

Correct Answer: C

Solution :

[c]

If  and if