To solve the problem of finding the ratio of upthrust (or buoyant force) in paraffin oil to that in water for a copper cube, we need to understand the concept of buoyancy and how it relates to the weight of the object in air and the weight of the object when submerged in a fluid. ### Step-by-Step Explanation 1. **Understanding Upthrust (Buoyant Force)**: - The upthrust (or buoyant force) experienced by an object submerged in a fluid is given by Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. - Mathematically, the upthrust \( U \) can be calculated as: \[ U = W_{\text{air}} - W_{\text{fluid}} \] where \( W_{\text{air}} \) is the weight of the object in air, and \( W_{\text{fluid}} \) is the weight of the object when submerged in the fluid. 2. **Calculating Upthrust in Paraffin Oil**: - Given: - Weight of the copper cube in air, \( W_{\text{air}} = 0.25 \, \text{N} \) - Weight of the cube in paraffin oil, \( W_{\text{oil}} = 0.17 \, \text{N} \) - The upthrust in paraffin oil \( U_{\text{oil}} \) is calculated as: \[ U_{\text{oil}} = W_{\text{air}} - W_{\text{oil}} = 0.25 \, \text{N} - 0.17 \, \text{N} = 0.08 \, \text{N} \] 3. **Calculating Upthrust in Water**: - Given: - Weight of the cube in water, \( W_{\text{water}} = 0.15 \, \text{N} \) - The upthrust in water \( U_{\text{water}} \) is calculated as: \[ U_{\text{water}} = W_{\text{air}} - W_{\text{water}} = 0.25 \, \text{N} - 0.15 \, \text{N} = 0.10 \, \text{N} \] 4. **Finding the Ratio of Upthrust in Oil to Upthrust in Water**: - Now we can find the ratio of the upthrust in oil to the upthrust in water: \[ \text{Ratio} = \frac{U_{\text{oil}}}{U_{\text{water}}} = \frac{0.08 \, \text{N}}{0.10 \, \text{N}} = \frac{8}{10} = \frac{4}{5} \] ### Conclusion The ratio of upthrust in paraffin oil to upthrust in water is \( \frac{4}{5} \). ### Explanation of Options - **Option A (3:5)**: This ratio does not match our calculated ratio of \( \frac{4}{5} \). - **Option B (4:5)**: This is the correct answer as it matches our calculated ratio. - **Option C (7:10)**: This ratio simplifies to \( \frac{0.7}{1} \), which is not equal to \( \frac{4}{5} \). - **Option D (13:10)**: This ratio is greater than 1, which does not correspond to our calculated values. ### Common Pitfalls - **Misunderstanding Buoyant Force**: Some students may confuse the buoyant force with the weight of the object itself. Remember, the buoyant force is the difference between the weight in air and the weight in the fluid. - **Incorrect Subtraction**: Ensure that you subtract the weight in the fluid from the weight in air correctly to find the upthrust. ### Revision Summary - The upthrust (buoyant force) is calculated as the difference between the weight in air and the weight in the fluid. - For the copper cube, the upthrust in paraffin oil is \( 0.08 \, \text{N} \) and in water is \( 0.10 \, \text{N} \). - The ratio of upthrust in oil to upthrust in water is \( \frac{4}{5} \). - The correct answer is Option B (4:5).