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 Main Online Paper ( Held On 11 Apirl  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) \[\frac{2L}{3}-\frac{{{\lambda }_{o}}{{L}^{2}}}{6M}\]