7328722 - Solution 1 P.4 Let m= mass of solid bounded above...

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1.4 P α Solution: Let m= mass of solid bounded above by ( ) = +. rho ρ 1 6cos φ and below by the sphere = . ρ 1 4 Density function: = , , = d dρ θ φ 10ρ2 For spherical system, the volume element, = dV ρ2sinφ dρ dφ dθ Mass of the solid is then given by: = , , . m θ1θ2φ1φ2ρ1ρ2dρ θ φ ρ2sinφ dρ dφ dθ Let α be the value of polar angle φ for which the upper and lower surfaces of the solid intersect. As shown in fig. a sphere with radius . 1 4 and a sphere with radius +. 1 6cos φ are drawn. The sphere will intersect at a point P at an angle . α At that instant radii are equal. +. = . 1 6cosα 1 4 . = . 0 6cosα 0 4 = .
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