2 kg at origin, 3 kg at x=5 cm, and 6 kg at x=10 cm. The distance of the centre of mass of the system from the origin is
Question
2 kg at origin, 3 kg at x=5 cm, and 6 kg at x=10 cm.
The distance of the centre of mass of the system from the origin is.
Solution
The center of mass (COM) of a system is given by the formula:
COM = (m1x1 + m2x2 + m3*x3) / (m1 + m2 + m3)
where m1, m2, m3 are the masses and x1, x2, x3 are their respective distances from the origin.
Here, m1 = 2 kg, m2 = 3 kg, m3 = 6 kg and x1 = 0 cm, x2 = 5 cm, x3 = 10 cm.
Substituting these values into the formula, we get:
COM = (20 + 35 + 6*10) / (2 + 3 + 6) = (0 + 15 + 60) / 11 = 75 / 11 = 6.82 cm
So, the center of mass of the system is 6.82 cm from the origin.
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