HardPhysics
+4 / -1
-- Particles of masses m, 2m, 3m, ... nm are placed on x axis at distances x = r, x = 2r, x = 3r, ... nr from origin. The distance of centre of mass of the system of particles from origin is
A
(n(n+1)/6)r
B
((2n+1)r)/3
C
((n(2n+3)r)/2)
D
(n^2(n+1)r)/2
Explanation
Xcm = Σmixi / Σmi = (m*r + 2m*2r + ... + nm*nr) / (m + 2m + ... + nm) = m*r*(1^2 + 2^2 + ... + n^2) / (m*(1 + 2 + ... + n)). Using series formulas: [n(n+1)(2n+1)/6] / [n(n+1)/2] * r = (2n+1)r/3.
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