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Standard XII

Physics

Angular Velocity

A solid spher...

Question

A solid sphere consist of mass M has radius R and a small spherical cavity of radius $(\frac{R}{4})$ is created from surface of sphere as shown in figure. The position of the centre of mass of the remaining mass of the sphere from O point is:

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Solution

$\frac{M}{m} = \frac{\int . \frac{4 π}{3} . R^{3}}{\int . \frac{4 π}{3} . {(\frac{R}{4})}^{3}} = 64 \Rightarrow M = 64 m x_{c m} = \frac{M x_{1} - m x_{2}}{M - m} = \frac{64 m \times 0 - m \times \frac{3 R}{4}}{64 m - m} = \frac{- 3 \frac{R}{4}}{63} = - \frac{R}{84}$

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A solid sphere consist of mass M has radius R and a small spherical cavity of radius (R4) is created from surface of sphere as shown in figure. The position of the centre of mass of the remaining mass of the sphere from O point is:

Mm=∫.4π3.R3∫.4π3.(R4)3=64⇒M=64 mxcm=Mx1−mx2M−m=64 m×0−m×3R464 m−m=−3R463=−R84

A solid sphere consist of mass M has radius R and a small spherical cavity of radius $(\frac{R}{4})$ is created from surface of sphere as shown in figure. The position of the centre of mass of the remaining mass of the sphere from O point is:

$\frac{M}{m} = \frac{\int . \frac{4 π}{3} . R^{3}}{\int . \frac{4 π}{3} . {(\frac{R}{4})}^{3}} = 64 \Rightarrow M = 64 m x_{c m} = \frac{M x_{1} - m x_{2}}{M - m} = \frac{64 m \times 0 - m \times \frac{3 R}{4}}{64 m - m} = \frac{- 3 \frac{R}{4}}{63} = - \frac{R}{84}$