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Find the position of centre of mass of t...

Find the position of centre of mass of the quarter solid sphere from 'C' in which mass per unit volume is given as `rho(r )=rho_(0)(1-(r )/(R ))`, where r is radial distance from centre and R is radius of solid quarter sphere

A

`(3)/(10)R`

B

`(3sqrt(2))/(7)R`

C

`(3sqrt(2))/(10)R`

D

`(3sqrt(2))/(5)R`

Text Solution

Verified by Experts

`y_(cm)=(int_(0)^(R )[rho_(0)(1-(r )/(R ))(2pi r^(2)dr)](r )/(2))/(int_(0)^(R )rho_(0)(1-(r )/(R ))(2pi r^(2))dr)`
`=((1)/(2)((R^(4))/(4)-(R^(5))/(5R)))/(((R^(3))/(3)-(R^(4))/(4R)))=(12)/(2).(R )/(20)=(3)/(10)R`
Position of C.M. from C
`=((3sqrt(2))/(10)R)`
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Knowledge Check

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