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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 :A. `((2n + 1)l)/(3)`B. `(l)/(n + 1)`C. `(n(n^2+1)l)/(2)`D. `(2 l)/(n(n^2 + 1))` |
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Answer» Correct Answer - A (a) `x_(cm) =(m l + 2ml 2 l + 3m 3 l...nmnl)/(m + 2m _+...+nm)` =`(l[1 + 4 + 9 +...+ n^2])/(1 + 2 + ...+ n)` =`(l[n (n + 1)(2n + 1)//6])/(n(n + 1)//2) = ((2n + 1)l)/(3)`. |
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