Question

Oil of density 800kgm^-3 rests on the surface of water. A cube block of side 50mm floats by a distance of 37.5mm in the fresh water as shown in the figure.

Determine.

1. the upthrust on the block due to water. 
2. the upthrust on the block due to oil.     
3. the weight of the block.      
4. the density of the cube block.   

Answer 1

1. U_w=v × P × g =0.05² ×0.0375×1000kg⁻³× 10NKg⁻¹
                        =9.375 × 10⁻¹N =0.9375N
2. U_oil  v × P × g = 0.05² × 0.0125 × 800kg × 10NKg⁻¹
                         = 2.5 × 10⁻¹N =0.52N
3. w=(99.375 +2.5) × 10⁻¹
      =1.188N
4. e_block =   mass     =  0.11875kg
                volume            0.05³
                             =950Kgm⁻³