Question

A metal cube of 5 cm edge and density 9 g cm^-3 is suspended by a thread so as to be completely immersed in a liquid of density 1.2 g cm^-3. Find the tension in the thread.(Take g= 10 ms^-2)

Answer 1

Edge of cube, l = 5 cm

Volume of cube V = l³ = 5³ = 125 cm³

= 125 × 10^–6 m³

Density of cube ρ_C = 9 g/cm³ = 9000 kg/m³

Density of liquid ρ_l = 1.2 g/cm³ = 1200 kg/m³

Tension in string (T) = Apparent weight of object

⇒ T = W – F_b

Where W = weight of object

F_b = Upthrust by fluid

T = mg – ρ₁ V g

= ρ_C Vg – ρ_l V g

= (ρ_C – ρ_l) V g

T = (9000 – 1200) × 125 × 10^–6 × 10

= 7800 × 125 × 10^–5

= 9.75 N