1.

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

Answer»

`(3)/(10)R`
`(3sqrt(2))/(7)R`
`(3sqrt(2))/(10)R`
`(3sqrt(2))/(5)R`

Solution :`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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