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

Step-by-step solution

Distance of centre of mass aligned x_ c m & = m₁ x₁+m₂ x₂+ m_n x_n m₁+m₂+ m_n & = m l+2 m 2 l+ n m n l m+2 m+3 m+ n m & = m l (1+4+9+ n^2 ) m(1+2+3+ n) 1+4+9 & + n^2= n^2 & = n(n+1)(2 n+1) 6 1+2+3+ & n= n= n(n+1) 2 x_ c m & = (n+1)(2 n+1) 6 = l(2 n+1) 3 aligned