A copper cube of mass 0.5 kg is weighed in water. The mass comes out to be 0.4 kg. Is the cube hollow or solid? [Density of copper=8.96*10^3 kg/m^3].
Does a hollow cube displace more water than solid cube of same mass?

Asked by arjunsah797 | 12th Mar, 2022, 11:10: AM

Expert Answer:

volume of 0.5 kg copper cube = mass / density = 0.5 / ( 8.96 × 10+3 ) = 5.58 × 10-5 m3
 
weight 0.5 kg copper cube in water = weight in air - loss of weight
 
weight 0.5 kg copper cube in water = weight in air - weight of displaced water
 
weight 0.5 kg copper cube in water = Volume displaced × ( ρC - ρW )
 
where ρC is density of copper and ρW is density of water
 
weight 0.5 kg copper cube in water = 5.58 × 10-5 × ( 8960 - 1000 ) = 0.444 kg
 
hence a solid copper cube of mass 0.5 kg should weigh 0.444 kg in water .
 
If a Copper cube of mass 0.5 kg weighs only 0.4 kg , then loss of weight in water is more .
 
Hence displaced volume that equals volume of given copper cube is greater ,
 
Hence given copper cube of mass 0.5 kg is hollow .
 
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Volume hollow cube is graeter than the solid cube of same mass .
 
Hence hollow cube will displace more water compare to solid cube of same mass.

Answered by Thiyagarajan K | 12th Mar, 2022, 12:26: PM