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A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm is removed from one edge as shown in the figure. The centre of mass of the remaining portion from the centre of the original plate will be(in cm).

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Best answer

New center of mass is given by:

\(x_{com} = \frac{m_1x_1 - m_2x_2}{m_1 - m_2}\)

where,

m1​ is mass of original disc

m2​ is mass of removed disc

x1​ is center of mass position of original disc

x2​ is center of mass position of removed disc

If mass per unit area=m then,

 mass of original disc = m × π × (28 × 10−2)2

mass of removed disc = m × π × (21 × 10−2)2

Center of mass shifts by 9 cm.

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