Question

A metal cube of edge 5cm and density 9.0 g$c{m}^{-3}$ is suspended by a thread so as to be completely immersed in a liquid of density 1.2 $c{m}^{-3}$. Find the tension in the thread.

(Take g = 10 m/$s^2$)

[Hint: Tension in thread = apparent weight of the cube in liquid]

Answer 1

Given:

Density of metal cube = 9.0 g$c{m}^{-3}$

Density of liquid = 1.2 g$c{m}^{-3}$

Side of the cube = 5cm

Volume of the cube = 5 x 5 x 5 = 125 $c{m}^3$

To find the weight of the cube:

Mass of the cube = volume of the cube x density of the cube

= 125 x 9 = 1125 g

∴ Weight of the cube = 1125 gf

The weight of the cube acts downwards

Upthrust acting on the cube = weight of the liquid moved

= volume of the cube x density of the liquid x g

= 125 x 1.2 x g = 150gf

Upthrust on the cube acts in the upward direction

Tension in thread = total force acting in the downward direction

= weight of the cube acting downwards – upthrust acting on the cube

= 1125 – 150 = 975gf or 9.75N