Particles of masses m, 2m, 3m, ... , nm grams are placed on the same line at distances l, 2l, 3l, ..., nl cm from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres is

Particles of masses m, 2m, 3m, ... , nm grams are placed on the same l

1.	Particles of masses m, 2m, 3m, ... , nm grams are placed on the same line at distances l, 2l, 3l, ..., nl cm from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres is
Answer» `((2N + 1) l)/(3)` `(l)/(n + 1)` `(n (n^2 + 1) l)/(2)` `(2L)/(n(n^2 + 1))` SOLUTION :`X_(CM) = (m_(1) x_(1) + m_(2) x_(2) +… + m_(n) x_(n))/(m_(1) + m_(2) + … + m_(n)) = (ML+ 2m * 2l + 3m * 3L + … + nm.nl)/(m + 2m + 3m + … +nm)` `= (m l (1 + 4 + 9 + … + n^2))/(m (1 + 2 + 3+ …+ n)) = ( l "" (n (n +1) ( 2n +1))/(6))/((n(n+1))/(2)) = (l (2n + 1))/(3)`