Answer to Question #178885 in Physics for Islam Helmy

Question

rectangular box has a width of 1 m, a length of 5 m and a mass of 1000 kg. Determine the mass should be added to be immersed to a depth of 250 mm in fresh water.

Answer 1

The box will be immersed in water to a depth of 0.25 m if the force of gravity is equal to the buoyancy force:

$$(m+M)g=\rho gV,\\ mg+Mg=\rho g(Ah),\\\space\\ m=\rho Ah-M=\\=1000·1·5·0.25-1000=250\text{ kg}.$$