Question

A stone of density 3000 kgm³ is lying submerged in water of density 1000 kgm³. If the mass of stone in air is 150 kg, calculate the force required to lift the stone. [g = 10 ms²]

Answer 1

Density of stone =ρ = 3000 kgm³
Density of water = ρ’ = 1000 kgm³
Mass of stone = m = 150 kg
Acceleration due to gravity = g = 10 ms^-2 

Volume of stone = V = `"m"/ρ`

V = `150/3000 = 1/20` = 0.05 m³ 

Actual weight of stone = mg = 150 x 10 = 1500 N
Volume of water displaced = Volume of stone
V = 0.05 m³
Mass of water displaced = m’ = V x p’
m’ = 0.05 x 1000 = 50 kg
Upthrust = m’g = 50 x 10 = 500 N
Force required to lift the stone
= Actual weight of stone – upthrust
= 1500 -500 = 1000 N