g An ancient bronze statue is discovered in a shallow part of the Mediterranean Sea and hoisted to the surface with a steel cable. The recovery team observes that the cable vibrates with a fundamental frequency of 203 Hz when the sculpture is hanging freely in the air, but a frequency of only 187 Hz when the sculpture was still submerged just below the surface. What is the density of the statue

Explanation:

Let the volume of bronze statue be V .

mass = vd where d is its density . If T₁ be the tension in cable when bronze statue hangs in air from it

T₁ = mg = vdg

when the statue is in water , tension in cable T₂

T₂ = v g ( d - 1 ) , density of water = 1 , here Tension reduces due to buoyant force acting on the statue .

If n be the frequency of cable when tension in it is T

n is proportional to √T .

1.178 = d / (d-1 )

1.178 d - 1.178 = d

.178 d = 1.178

d = 6.6 gm / cc

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