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

Answer

A

Explanation

Ans.(1)
Distance of centre of mass `X_(cm)=(summ_(1)x_(1))/(summ_(1))`
`(ml+2m(2l)+3m(3l)+.....+(nm)(nl))/(m+2m+3m+.....+nm)`
`((l^(2)+2^(2)+3^(2)+.....+(n^(2)))/(1+2+3+.....+n))l=(2n(n+1)(2n+1))/(6(n)(n+1))l`
`=((2n+1))/(3)l`