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Question

All the particles of a body are situated at a distance R from the origin. The distance of the centre of mass of the body from the origin is
(a) = R
(b) ≤ R
(c) > R
(d) ≥ R


Solution

(b) ≤ R

Distance of the centre of mass from the origin is given by,
R' = 1Mi=1nmiri

Let half of the particles lie on +Y-axis and the rest of  the particles lie on +X-axis.
YCM = m3Rj+ m4Rjm1 + m2 + m3 + m4 +...       = Rj2

Similarly, XCM = Ri2

Therefore, the coordinates of centre of mass are R2,R2.

Distance of the centre of mass from the origin=R2   
For the given situation,  R'<R.           

In general, R'R.

Physics
HC Verma - I
Standard XI

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