Question

A block of wood is made to float separately in river water and then in ocean water. The weight of the displaced river water is
A. Equal to the weight of the displaced ocean water
B. less than the weight of the displaced ocean water
C. more than the weight of the displaced ocean water
D. not dependent on the density of wooden block

Answer 1

Archimedes principle is the greatest invention which helps to solve the problems in fluid mechanics. It deals with the weight of the fluid displaced when an object is immersed inside the fluid and a new term called buoyancy force came into existence after that. Based on this concept only we solve this problem.

Complete Answer:
Usually, when we immerse an object in the water then that object will displace some volume of the water and that will float on the water. That is floating in the sense it is in equilibrium which means forces are balanced. Weight will be always acting downwards but the object is not moving down it is floating which means there must be a force acting upwards which balances this weight and that force is called buoyancy force.
According to Archimedes principle the weight of the fluid displaced will be equal to the buoyancy force acting on the object.
Now from the question, when an object floats in the river water the buoyancy force is balanced by the weight of the block. When the block is floating on the ocean water then the buoyancy force is balanced by the weight of the block. If we carefully observe in both cases the buoyant forces are getting balanced by the weight of the body.
Weight of the body is constant and doesn’t change which means the buoyancy force given by the two fluids is also the same which implies that the weight of the displaced water will be the same in both cases.

Hence answer would be option A.

Note:
Even though buoyancy force is same in both the cases the volume of the liquid displaced in both the cases would be different, because the product of liquid density and volume displaced will be same which doesn’t mean that the volume displaced must be same in both the cases. Buoyancy force always acts against the resultant acceleration.