Question

A sphere of solid material of relative density 9 has a concentric spherical cavity and just sinks in water. If the radius of sphere be r, then the radius of cavity (r) will be related to r as

Answer 1

Step-by-step explanation:

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here is you answer

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according to the law of floatation

a body floats if weight of the body is equal to the weight of water displayed

            weight of the sphere =weight of the water displaced

          4/3π(R^3-r^3)*9 pw=4/3πr^3pw

              9(R^3-r^3)=R^3

             r^3=8/9r^3

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Answer 2

Dear Student,

◆ Answer -

2R/9^(1/3)

● Explanation -

For the sphere to just sink, weight of the sphere should be equal to weight of water displaced. Let r be the radius of the cavity and R be the radius of the sphere.

Ws = Ww

Vs × ds × g = Vw × ds × g

4π/3 (R^3-r^3) × ds × g = 4π/3 R^3 × dw

4π/3 (R^3-r^3) × 9dw = 4π/3 R^3 × dw

9 (R^3-r^3) = R^3

9R^3 - 9r^3 = R^3

9R^3 - R^3 = 9r^3

8R^3 = 9r^3

r^3/R^3 = 8/9

r/R = 2/ 9^(1/3)

r = 2R / 9^(1/3)

Hence, ratio of inner radius to outer radius is 2R/ 9^(1/3).

Thanks dear. Hope this helps you..