A sphere of solid material of specific gravity 8

Asked by admin @ 16/08/2021 in Physics viewed by 287 People

A sphere of solid material of specific gravity 8 has a concentric spherical cavity and just sinks in water. Then, the ratio of the radius of the cavity to the outer radius of the sphere must be

Answered by admin @ 16/08/2021

Dear Student,

◆ Answer -

r/R = 7^(1/3)/2

● Explanation -

For the sphere to just sink, weight of the sphere should be equal to weight of water displaced.

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) × 8dw = 4π/3 R^3 × dw

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

8R^3 - 8r^3 = R^3

8R^3 - R^3 = 8r^3

7R^3 = 8r^3

r^3/R^3 = 7/8

r/R = 7^(1/3)/2

Hence, ratio of inner radius to outer radius is 7^(1/3)/2.

Thanks dear. Hope this helps you..

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