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when a metal sphere is dropped in to a tall cylinder containing liquid its acceleration is g÷2 (gravity over 2) show that : density of metal =2density of liquid​

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ONYEBUCHINNAJIGO

The density of the metal sphere is 2 times the density of the liquid as proved.

Net upward force acting on the metal sphere

The net upward force acting on the sphere as it is dropped into the liquid is calculated as follows;

F =  σVg - ρVg

ma =  σVg - ρVg  

where;

  • ρ is density of the liquid
  • σ is the density of the metal
  • a is acceleration of the metal

σV(a) =  σVg  - ρVg

σ(a) = σg  - ρg

σ(g/2) = σg -  ρg  

g(σ/2) = g(σ -  ρ)

σ/2 = σ -  ρ

σ/2 - σ = -  ρ

-σ/2 = -  ρ

σ = 2ρ

Thus, the density of the metal sphere is 2 times the density of the liquid as proved.

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