A solid lump of iron weighs 300N in air and 262N in water. Find its volume.?

Question

I know the answer, i just want to see how its worked out

Answer 1

What's the water got to do with it ?
(EDIT = OK, so it's a displacement Q .. but this means knowing the density of water instead of the density of the iron = so I guess it depends which is the most 'pure')


Using Newton's second law, F = ma (force = mass × acceleration). Here, F is 300N, m is the Mass of the Iron, and a is the acceleration due to gravity (on Earth approximately 9.8 m/s), so we have :-

300 = 9.8 x Mass of Iron.

Mass of Iron = 300 / 9.8 = 30.61 kg.

Density of iron (at room temp) is 7.86 g·cm−3 (from wikipedia), so we have 30.61 / 7.86 cubic meters = 3.8947 cu.m (or approx 3,895 cu. cm)

Answer 2

The difference is brought abought by displacement of water; in this case 300-262 = 38, thus the displaced water weighs 38N.

One newton = one Kg accelerated at 1 m/s/s, and gravity = 9.811 m/s/s - therefore the mass of water displaced is 38/9.811 Kg = 3.8732 Kg (3873.2 grams).

Since pure water has a density of 1 gram per cubic centimetre, that's a total of 3873.2 cm3 of water displaced - this would also therefore be the volume of the solid body concerned.

I hope this helps, but please feel free to drop me a line if you'd like to discuss this or any other figure-work further.

Answer 3

300N-262N = 38N
This is the upthrust given by the water which is also the weight of the water displaced.
Pure water has a density of 1g/cm3 approx
1N=100g approx so 38N=3800g=3800cm3