A copper cube weighs 0.25 N in air, 0.17N when completely immersed in paraffin oil and 0.15 N when completely immersed in water.The ratio of upthrust in oil...

A copper cube weighs 0.25 N in air, 0.17N when completely immersed in paraffin oil and 0.15 N when completely immersed in water.The ratio of upthrust in oil to upthrust in water is

Answer Details

The upthrust on a submerged object is equal to the weight of fluid displaced by the object. The weight of an object in a fluid is given by the difference between the weight of the object in air and the upthrust on the object in that fluid. Let's call the weight of the copper cube in air W. Then, the upthrust in paraffin oil is (W - 0.17 N), and the upthrust in water is (W - 0.15 N). Now, we can use the fact that the ratio of upthrust in oil to upthrust in water is equal to the ratio of the weight of water displaced to the weight of oil displaced. Let's call the weight of water displaced Ww and the weight of oil displaced Wo. Then, we have: (W - 0.17 N)/(W - 0.15 N) = Ww/Wo Simplifying this expression by cross-multiplying, we get: (W - 0.17 N) * Wo = (W - 0.15 N) * Ww Expanding the brackets, we get: Wo * W - 0.17 N * Wo = Ww * W - 0.15 N * Ww Rearranging this expression, we get: (Ww/Wo) = (W - 0.17 N)/(W - 0.15 N) Substituting the given values, we get: (Ww/Wo) = (0.25 N - 0.17 N)/(0.25 N - 0.15 N) = 0.08 N/0.10 N = 4/5 Therefore, the ratio of upthrust in oil to upthrust in water is 4:5, which is option (B).