question_answer

A thin bar of length L has a mass per unit length \[\lambda \], that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is \[{{\lambda}_{O}},\] then the distance of the centre of mass from the lighter end is:                                                                                          [JEE ONLINE 11-04-2014]

A)  \[\frac{L}{2}-\frac{{{\lambda }_{o}}{{L}^{2}}}{4M}\]          

B)       \[\frac{L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{8M}\]

C)  \[\frac{L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{4M}\]

D)       \[\frac{2L}{3}-\frac{{{\lambda }_{o}}{{L}^{2}}}{6M}\]