Question

n particles of masses M 2m 3M and 4m grams are placed on the same line and distance L 2 L 3 l 4l cm from a fixed point the distance of a centre of mass of the particles from a fixed point in centimetre is​

Answer 1

Answer:

Explanation:

Given N particles of masses m 2 m 3 m and 4 m grams are placed on the same line and distance L 2 L 3 l 4 l cm from a fixed point the distance of a centre of mass of the particles from a fixed point in centimetre is

Distance of centre of mass from o will be  

          = m l + 2 m x 2l+---------------+ nm x nl / m + 2m+----------------nm

       = m l (1 + 2^2 +-------------n^2 ) / m(1 + 2 + -------------n)

       = sum of squares of natural numbers / sum of natural numbers.

          =  l (n(n + 1) (2n + 1)  1/6 )/ n(n + 1) / 2

          = 1/3 (2n + 1)  l

Answer 2

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