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 metal cube = 5 cm.
Density of the metal cube = 9 gcm^-3 = 9 × 10³ kgm^-3.
Volume of the metal cube = 125 cm³ = 125 × 10^-6 m³.
Mass of the metal cube =9 × 10³ ×125 × 10^-6 = 1125 × 10^-3 =1.125 kg.
Weight of the liquid = mass × gravity = 1.125 × 10 = 11.25 N.
Density of liquid = 1.2 gcm^-3= 1.2 × 10³ kgm^-3.
Upthrust of the liquid = V × p × g.
Upthrust = 125 × 10-6 × 1.2 × 103 × 10 = 1.5 N.
The apparent weight of the body = weight of liquid - upthrust
Apparent weight = 11.25 N - 1.5 N = 9.75 N
Tension in the string is equal to the apparent weight of the body
So, the tension in the string would be 9.75 N.