What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are ρ and σ respectively, and the viscosity of the liquid is η).

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r2g9η(ρ−2σ)

r2g9η(2ρ−σ)

r2g9η(ρ−σ)

2r2g9η(ρ−σ)

answer is A.

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Detailed Solution

Fwt=W-FB-FV ma=4πr3ρbg3-4πr3ρlg3 4πr3ρb3a=4πr3ρb-ρlg3-6πηrνT vT=r2g9η(ρ−2σ)

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