Block A weighs 12 N and has an apparent weight of 8 N when completely submerged in an ideal fluid. Block B weighs 20 N and has an apparent weight of 12 N when completely submerged in the same ideal fluid.

The ratio of the densities A / B equals:

density of block A to density of block B = 2 / 3

Also density of block B to density of block A = 3 / 2

Explanation:

Given:

Weight of block A = 12 N

Apparent weight of block A = 8 N Weight of block B = 20 N

Apparent weight of block B = 12 N

Upthrust in the fluid = density of block x volume of fluid x gravity

In equilibrium condition; upthrust in fluid = weight of the block in fluid

Weight of the block = density of block x volume of fluid x gravity

For constant volume of the fluid;

Volume = Weight / (density x gravity)

For block A: weight when completely submerged in fluid = 8N

Volume = (8) / (density of A x gravity)

For block B

Volume = (12) / (density of B x gravity)

At same fluid volume:

(8) / (density of A x gravity) = (12) / (density of B x gravity)

(8/12) = (density of A x gravity) / (density of B x gravity)

density A / density B = 2 / 3

Therefore, density of block A to density of block B is 2/3.

Also density of block B to density of block A is 3 / 2