An ice cube with a small iron ball in its centre is placed in a cup of water. 3.9 x 10-3kg of water in the cup is displaced and the volume of the ice cube is 4.0 x 10-6m3. Ice density: 1000 kg m-3 Iron density: 7800 kg m-3, what is the volume of the iron?

Firstly you need to know that the weight/mass of water displaced by the cube is equal to the weight/mass of the ice cube: 3.9 x 10-3kg You then need to recognise that the weight of the cube is the weight of the iron ball added to the weight of the ice.  Where the volume of the iron ball is V, the weight of the iron ball is the volume of the iron ball multiplied by the density iron: V x 7800 kg m-3.
The weight of the ice will be the volume of the ice (the total volume of the ice cube minus the volume of the iron) multiplied by the density of iron: (4 x 10-6m3– V) x 920 kg m-3 Hence mass of the ice cube = mass of ice + mass of iron
3.9 x 10-3= ((4 x 10-6– V) x 920) + (V x 7800) 3.9 x 10-3= (3.68 x 10-3-920V) + 7800V (3.9 x 10-3) – (3.68 x 10-3) = 6880V 2.2 x 10-4= 6880V V = 3.2 x 10-8 Volume of iron ball = 3.2 x 10-8m3

Answered by Adam C. Physics tutor

7717 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What are the similarities and differences between gravitational and electric fields?


You have a layer of glass with a refractive index of 1.5 and the glass is surrounded by air. A light ray shines into the glass and Total Internal Reflection occurs at the glass-air boundary. What is the critical angle?


Why does an electric drill heat up when passing through metal compared to in thin air?


You are in a vacuum chamber, and you drop a feather and a bowling ball (initially at rest) from a great height. Which will hit the ground first?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences