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A tank containing water is placed on a s...

A tank containing water is placed on a spring balance. A stone of weight w is hung and lowered into the water without touching the sides and the bottom of the tank. Explain how the reading will change.

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The situation is shown in figure. Make free-body diagrams of the bodies separately and consider their equilibrium. Like all other forces, buoyancy is also exerted equally on the two bodies in contact. Hence it the water exerts a buoyant force, say, B on the stone upward, the stone exerts the same force on the water downward. The forces acting on the 'water+ container' system are : W, weight of the system downward, B, buoyant force of the stone downard, and the force R of the spring in the upward direction. For equilibrium
R=W+B

Thus the reading of the spring scale will increase by an amount equal to the weight of the liquid displaced, that is, by an amount equal to the buoyant force.
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