Question

A cube of wood floating in water supports a 200g mass at the centre of its top face. When the mass is removed, the mass rises by 2cm. Determine the volume of cube.

(a) 1000cm^3

(b) 100cm^3

(c) 10cm^3

(d) 1cm^3

The question was posed to me in an interview.

Query is from Buoyancy topic in chapter Mechanical Properties of Solids of Engineering Physics I

Answer 1

Correct answer is (a) 1000cm^3

Easiest explanation: Let the side of the cube be l cm. As the mass 200g is removed, the cube rises by 2 cm. So by law of floatation,

Upthrust on cube due to displaced volume of water = 200gf

l×l×2×l×g=200×g

l^2=100

So, l=10cm

Therefore, volume of the cube = 10^3=1000cm^3.