Methods to locate centre of mass

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Question

A uniform metal disc of radius R is taken and out of it a disc of diameter R is cut off from the end. The centre of mass of the remaining part will be

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Solution

$\begin{array}{l} C entre of mass of the uncut disc is at O. \\ {Let the position of centre of mass of the remaining disc is C}_{1} and \\ {the positon of centre of mass of the removed disc is C}_{2} . \\ A p p l y i n g law of moments about O \\ s (mass of remaining disc) = \frac{R}{2} (m a s s of removed disc) \\ s [σ (π R^{2} - \frac{π R^{2}}{4})] = \frac{R}{2} [σ \frac{π R^{2}}{4}] \\ s = \frac{R}{6} \end{array}$

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Methods to locate centre of mass

Remember concepts with our Masterclasses.

A uniform metal disc of radius R is taken and out of it a disc of diameter R is cut off from the end. The centre of mass of the remaining part will be

Centre of mass of the uncut disc is at O.Let the position of centre of mass of the remaining disc is C1 and the positon of centre of mass of the removed disc is C2.Applying law of moments about Osmass of remaining disc=R2mass of removed discsσπR2−πR24= R2σπR24 s=R6

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