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When `n` number of particles of masses `m, 2m, 3m, …….. nm` are at distances `x_(1)=1, x_(2)=4, x_(3)=9, ………x_(n)=n^(2)` units respectively from origin on the x-axis, then find the distance of their centre of mass from origin.

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To find the distance of the center of mass of `n` particles with masses `m, 2m, 3m, ..., nm` located at distances `x_1 = 1, x_2 = 4, x_3 = 9, ..., x_n = n^2` from the origin on the x-axis, we can follow these steps: ### Step 1: Identify the masses and positions of the particles The masses of the particles are: - Mass of particle 1: \( m \) - Mass of particle 2: \( 2m \) - Mass of particle 3: \( 3m \) - ... ...
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