Question

A block 2cm x 5cm x 6cm high with a mass of 51 grams is placed in a fluid with a density of 1100 kg/m^3. Will the wood sink or float? If it floats, where is the water level on the block? IF it sinks, what is its acceleration?

Answer #1

here,

the volume of block , V = 2 cm * 5 cm * 6 cm

V = 60 cm^3 = 60 * 10^-6 m^3

mass , m = 51 g = 0.051 kg

the density of block , p1= m /V

p1 = 0.051 /(60 * 10^-6) kg/m^3

p1 = 850 kg/m^3

as the density of box is less than fluid

the box will float

let the height of water level be h'

equating the forces vertically

buoyant force = weight

density of liquid * volume submerged * g = m * g

1100 * ( 0.02 * 0.05 * h') = 0.051

h' = 0.0463 m = 4.63 cm

the water level in the block is 4.63 cm

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