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Centre Of Mass Of Solid Hemisphere MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

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Position of centre of mass for solid Hemisphere

Have a look at the figure of solid Hemisphere

Since it is symmetrical about y-axis  

So we can say that  its x_{cm} = 0 and z_{cm} = 0

Now we will calculate its y_{cm} which is given by

y_{cm} = \frac{\int y.dm}{\int dm}

So Take a small elemental hollow hemisphere of mass dm of radius r   as shown in figure.

Now have a look on elemental hollow hemisphere of mass dm of radius r

Since our element mass is hollow hemisphere so its C.O.M is at (r/2)

Now     dm=\rho dv=\rho (2\pi r^2)dr 

Where,     \rho =\frac{M}{\frac{2}{3}\pi R^3}

  y_{cm}=\frac{\int \frac{r}{2}dm}{M}=\frac{\int_{0}^{R}\frac{r}{2}*\frac{3M}{2\pi R^3}*2\pi r^2dr}{M}=\frac{3}{2R^3}* \int_{0}^{R}r^3dr=\frac{3R}{8}

 

So  y_{cm} = \frac{3R}{8} from base 

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Position of centre of mass for solid Hemisphere

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