A body partly immersed, floats in a liquid concentained in a beaker. The beaker is kept inside a lift falling freely under gravity. The upthrust on the body due to liquid is

Options

A. zero
B. equal to weight of body in air
C. equal to weight of liquid displaced
D. equal to weight of immersed part of body

Answer

To solve the problem of the upthrust on a body partly immersed in a liquid contained in a beaker that is falling freely under gravity, we can follow these steps:

### Step 1: Understand the Concept of Upthrust
Upthrust (or buoyant force) is the upward force exerted by a fluid on a body immersed in it. According to Archimedes' principle, the upthrust on a body is equal to the weight of the liquid displaced by the body.

### Step 2: Analyze the Situation in the Falling Lift
When the beaker is in a lift that is falling freely, both the beaker and the liquid inside it are in a state of free fall. This means that they are accelerating downwards at the same rate as gravity (g).

### Step 3: Determine the Apparent Weight of the Body
In a freely falling system, the apparent weight of the body becomes zero. This is because both the body and the liquid are accelerating downwards at the same rate, leading to a situation where the body does not exert any force on the liquid.

### Step 4: Apply Archimedes' Principle
Since the body does not exert any force on the liquid, it does not displace any liquid. According to Archimedes' principle, if no liquid is displaced, the upthrust (buoyant force) acting on the body is also zero.

### Step 5: Conclusion
Therefore, the upthrust on the body due to the liquid when the beaker is falling freely is zero.

### Final Answer
The upthrust on the body due to the liquid is **0**.

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