A sphere of relative density σ and diameter D has concentric cavity of diameter d . The ratio of d D , if it just floats on water in a tank is :

Question

A sphere of relative density σ and diameter D has concentric cavity of diameter d . The ratio of d D ​ , if it just floats on water in a tank is :

TestHub · Accepted Answer

weight ( w ) = 3 4 ​ π ( 8 D 3 − d 3 ​ ) σ g Buoyant force ( F b ​ ) = 1 × 3 4 ​ π ( 8 D 3 ​ ) ⋅ g For Just Float ⇒ w = F b ​ ​ ⇒ ( D 3 − d 3 ) σ = D 3 ⇒ 1 − D 3 d 3 ​ = σ 1 ​ ⇒ 1 − σ 1 ​ = ( D d ​ ) 3 ⇒ ( σ − 1 σ ​ ) 3 1 ​ = ( d D ​ ) ​

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