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Bucket A contains only water; an identical bucket B contains water, but also contains a solid object in the water. Consider the following four situations: (a) The object floats in bucket B, and the buckets have the same water level. (b) The object floats in bucket B, and the buckets have the same volume of water. (c) The object sinks completely in bucket B, and the buckets have the same water level. (d) The object sinks completely in bucket B, and the buckets have the same volume of water. In each of the above situations, which bucket has the greater total weight? (A) Bucket A (B) Bucket B (C) Both buckets have the same weight. (D) The answer cannot be determined from the information given.

Bucket A contains only water; an identical bucket B contains water, but also contains a solid object in the water. Consider the following four situations: (a) The object floats in bucket B, and the buckets have the same water level. (b) The object floats in bucket B, and the buckets have the same volume of water. (c) The object sinks completely in bucket B, and the buckets have the same water level. (d) The object sinks completely in bucket B, and the buckets have the same volume of water. In each of the above situations, which bucket has the greater total weight?
(A) Bucket A
(B) Bucket B
(C) Both buckets have the same weight.
(D) The answer cannot be determined from the information given.

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
(a) The correct option is (C).
According to Archimedes’ principle, the buoyant force acting on the solid object in the bucket B is equal to the volume of the water displaced by the solid object.
It is given that the water levels in both the bucket A and B is same. This means the total weight in both the bucket is same. Therefore, option (C) is correct.
(b) The correct option is (B).
It is given that the volumes of the water in the buckets are same. As the mass of the water is the volume times the density of the water, the mass of the water in the buckets are the same. Addition of solid object in the bucket B will definitely increase the total mass in the bucket. This means the total weight in the bucket B is greater than in the bucket A. Therefore, option (B) is correct.
(C) The correct option is (B).
It is given that the object sinks in the bucket B. So, the density of the solid object is greater than the density of the water. It also means the volume of the solid occupied the same volume of water in the bucket B. But the level of water in both the buckets is the same. It can be inferred that the total weight of the bucket B might be greater than the bucket A. Therefore, option (B) is correct.
(d) The correct option is (B).
It is given that the volumes of the water in the buckets are same. As the mass of the water is the volume times the density of the water, the mass of the water in the buckets are the same. It is also given that the solid object sinks in the bucket B. So, addition of solid object in the bucket B will definitely increase the total mass in the bucket. This means the total weight in the bucket B is greater than in the bucket A. Therefore, option (B) is correct.

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