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Q.

One end of a thin uniform rod length L and mass $M_{1}$ is rivetted to the center of a uniform circular disc of radius 'r' and mass $M_{2}$ so that both are coplanar. The center of mass of the combination from the center of disc is (Assume that the point of attachment is at the origin )

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a

$\frac{L (M_{1} + M_{2})}{2 M_{1}}$

b

$\frac{{LM}_{1}}{2 (M_{1} + M_{2})}$

c

$\frac{2 (M_{1} + M_{2})}{{LM}_{1}}$

d

$\frac{2 {LM}_{1}}{(M_{1} + M_{2})}$

answer is B.

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Detailed Solution

Question Image

$x_{cm} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

$= \frac{M_{2} (0) + M_{1} (\frac{L}{2})}{M_{1} + M_{2}}$

$= \frac{M_{1} L}{2 (M_{1} + M_{2})}$

$x_{cm} = \frac{{LM}_{1}}{2 (M_{1} + M_{2})}$

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One end of a thin uniform rod length L and mass M1 is rivetted to the center of a uniform circular disc of radius 'r' and mass M2 so that both are coplanar. The center of mass of the combination from the center of disc is (Assume that the point of attachment is at the origin )