Particle of masses `m, 2m,3m,…,nm` grams are placed on the same line at distance `l,2l,3l,…..,nl cm` from a fixed point. The distance of centre of mass of the particles from the fixed point in centimeters is :

Options

A. `((2n+1)l)/3`
B. `l/(n+1)`
C. `(n(n^(2)+l)l)/2`
D. `(2l)/(n(n^(2)+l)l)`

Answer

A

Explanation

`x_(cm)=(Summx)/(Summ)=((1^(2)+2^(2)+3^(2)+...+n^(2))l)/((1+2+3+...++n))`