An object is floating in a liquid , kept in a container . The container is placed in a lift . Choose the correct option .

Options

A. Buoyant force increases as the lift accelerates up
B. Buoyant force decreases as the lift accelerates up
C. Buoyant force remains constant as the lift accelerates
D. The fraction of solid submerged into liquid decreases

Answer

To solve the problem of an object floating in a liquid inside a container placed in a lift, we need to analyze the effects of the lift's acceleration on the buoyant force acting on the object. Here’s a step-by-step breakdown:

### Step 1: Understanding the Scenario
- An object is floating in a liquid inside a container.
- The container is placed in a lift (elevator), which can accelerate either upwards or downwards.

### Step 2: Buoyant Force Concept
- The buoyant force (B) acting on the object is given by Archimedes' principle:
\[ B = V \cdot \rho \cdot g \]
where \(V\) is the volume of the liquid displaced by the object, \(\rho\) is the density of the liquid, and \(g\) is the acceleration due to gravity.

### Step 3: Effective Gravity in the Lift
- When the lift accelerates upwards with acceleration \(A\), the effective acceleration due to gravity (\(g_{effective}\)) becomes:
\[ g_{effective} = g + A \]
- Conversely, if the lift accelerates downwards, the effective gravity becomes:
\[ g_{effective} = g - A \]

### Step 4: Effect of Lift Acceleration on Buoyant Force
- If the lift accelerates upwards:
- The buoyant force increases because \(g_{effective}\) increases.
- Thus, the buoyant force acting on the object becomes:
\[ B = V \cdot \rho \cdot (g + A) \]

- If the lift accelerates downwards:
- The buoyant force decreases because \(g_{effective}\) decreases.
- The buoyant force acting on the object becomes:
\[ B = V \cdot \rho \cdot (g - A) \]

### Step 5: Floating Condition
- For the object to float, the buoyant force must equal the weight of the object:
\[ B = mg \]
- As the lift accelerates, the buoyant force changes, but the object will still float as long as the buoyant force equals the weight of the object.

### Step 6: Conclusion
- The buoyant force will increase as the lift accelerates upwards and decrease as it accelerates downwards. However, the fraction of the object submerged does not change because it depends on the density of the liquid and not on the effective gravity.

### Final Answer
- The correct option is that the buoyant force increases as the lift accelerates upwards.