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Bucket A holds only water. An identical bucket B holds water plus a solid object placed in the water. For each situation below, decide which bucket weighs more. Match Column-I with Column-II. Column-I: (A) The object floats in B, and both buckets have the same water level. (B) The object floats in B, and both buckets have the same volume of water. (C) The object sinks fully in B, and both buckets have the same water level. (D) The object sinks fully in B, and both buckets have the same volume of water. Column-II: (P) Bucket A is heavier (Q) Bucket B is heavier (R) Both weigh the same (S) Cannot be determined from the given information

1. A-R, B-Q, C-Q, D-Q
2. A-Q, B-P, C-R, D-S
3. A-R, B-R, C-Q, D-P
4. A-P, B-R, C-Q, D-S

Correct answer: A-R, B-Q, C-Q, D-Q

Solution

(A) Floating, same water level: a floating object displaces water equal to its own weight, so a column of water of the same level/shape weighs exactly the same as water+floating object. Both equal -> R. (B) Floating, same volume of actual water: B has the same water plus the object on top, so B is heavier -> Q. (C) Sunk, same water level: the submerged object occupies volume that would otherwise be water, but the solid (which sank, so denser than water) is heavier than the displaced water, so B is heavier -> Q. (D) Sunk, same volume of water: B = same water + whole object, clearly heavier -> Q. Thus A-R, B-Q, C-Q, D-Q.

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