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Center of Mass as an Average Point

By symmetry h...

Question

By symmetry how can we say that x_cm=0 or y_cm=0 in centre of mass

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Solution

Dear Student

$c e n t r e o f m a s s o f s y s t e m i s R_{c m} = \frac{m 1 r 1 + m 2 r 2}{m 1 + m 2} a t t h e c e n t e r r 1 = r 2 = 0 t h e n x_{c m} = \frac{m 1 x 1 + m 2 x 2}{m 1 + m 2} = \frac{m 1 \times 0 + m 2 \times 0}{m 1 + m 2} = 0 y_{c m} = \frac{m 1 y 1 + m 2 y 2}{m 1 + m 2} = \frac{m 1 \times 0 + m 2 \times 0}{m 1 + m 2} = 0$

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