calculate weight

Question

A stone of mass 3kg and density 2gcm-3 is suspended by a spring from a spring balance. the stone is completely submerged in a liquid of density 1.3gcm-3. calculate the weight that the balance reads given that acceleration due to gravity is 10kgm-3

Answer 1

The information given for the acceleration of gravity is not correct.  It may be approximated by 10 m/s², not 10 kg/m³.  Anyway,

 

g = acceleration of gravity

m = mass of the solid (given)

ρ_l = density of liquid (given)

ρ_s = density of solid (given)

 

V = volume of displaced liquid = volume of submerged solid = m/ρ_s

 

F_b = buoyant force = ρ_lVg 

 

F = force read by spring balance (this is what you want to find) = ?

 

F + F_b = mg

 

F = mg - F_b = mg - ρ_lVg = mg - ρ_l(m/ρ_s)g = mg(1 - ρ_l/ρ_s)

 

F = mg(1 - ρ_l/ρ_s)

 

Now just plug in the numbers and get F.