A hemi-spherical cavity is created in solid sphere (of radius `2R`) as shown in the figure. Then

Options

A. `x_(cm) = -R//15`
B. `y_(cm) = -(R)/(40)`
C. `z_(cm) = zero`
D. None of these

Answer

A, B, C

Explanation

`x_(cm)=((4)/(3)pi(2R)^(3)0-(2)/(3)piR^(3)R)/((4)/(3)pi(2R)^(3)-(2)/(3)piR^(3))=-(R)/(15)`
`y_(cm)=((4)/(3)pi(2R)^(3)0-(2)/(3)piR^(3)(3R)/(8))/((4)/(3)pi(2R)^(3)-(2)/(3)piR^(3))=-(R)/(40)`
`z_(cm) = 0`