A breaker containing water of weight W is placed on a spring balance. A stone weight W is hung and lowered into the water without touching the sides  and bottom of the breaker. Then the  tension in the string is

Physics Problem: Tension in String with Buoyant Force

1. Initial Setup

• Beaker with water: Weight = W
• Spring balance: Shows the weight of the beaker + water = W (assuming the beaker is massless or its mass is included in W)
• Stone: Weight = W (but it's not inside the water yet)

2. Stone Lowered into the Water

When the stone is lowered into the water without touching the sides and bottom, two forces act on it:

• Weight (W): Acting downward.
• Buoyant force (B): Acting upward.

Buoyant Force

The buoyant force is equal to the weight of the displaced water:

B = Weight of displaced water

3. Tension in the String

The stone is in equilibrium, so the forces balance:

T + B = W
⇒ T = W - B

where T is the tension in the string.

4. What Happens to the Spring Balance?

• Before: Shows weight of beaker + water = W
• After: The water level rises due to the displaced water, but the total weight measured by the spring balance is:
  • Beaker + water + weight of displaced water (since the buoyant force is transmitted to the beaker as a reaction force).
• But: Actually, the buoyant force means the stone is "lighter" by the weight of the displaced water, so the spring balance will show:
  • Original weight (W) plus no extra weight (the stone is held by the string, not resting on the beaker).
• Wait: Let's clarify this point.

Actually, the spring balance shows the weight of the beaker + water + the effect of the buoyant force.
But in reality, since the stone is not touching the beaker, the only extra force is the buoyant force acting on the water (which is a reaction force to the buoyant force on the stone).
But the spring balance is measuring the beaker + water + the stone's effect on the water.

However, the question asks for the tension in the string, not the spring balance reading.