A piece of iron of density 7.8×103 kg m−3 and volume 100 cm3 is totally immersed in water (ρ = 1000 kg m−3). Calculate its apparent weight in water.
6.8 N
Given,
Volume of iron piece = 100 cm3 =100×10−6m3=10−4m3
Weight of iron piece in air = Volume × density of iron × g
Weight of iron piece in air =10−4×(7.8×103)×10
Weight of iron piece in air = 7.8 N
Upthrust = (Volume of water displaced) × density of water ×g
But volume of water displaced = Volume of iron piece when it is completely immersed = 10−4m3
Upthrust = 10−4×1000×10=1N
Apparent Weight = True weight – Upthrust = 7.8–1 = 6.8 N.