Problem 10 - University Physics with Modern Physics

Question

A beaker is filled with water to the rim. Gently placing a plastic toy duck in the beaker causes some of the water to spill out. The weight of the beaker with the duck floating in it is a) greater than the weight before adding the duck. b) less than the weight before adding the duck. c) the same as the weight before adding the duck. d) greater or less than the weight before the duck was added, depending on the weight of the duck.

Step-by-Step Solution

Answer

Answer: c) The weight of the beaker with the duck floating in it is the same as the weight before adding the duck.

Step 1: Evaluating Option A

Option A suggests that the weight of the beaker with the duck floating in it is greater than the weight before adding the duck. This is not true, as the duck displaces its own weight in the water, and some of the water spills out. The weight of the beaker after placing the duck is equal to the weight of the beaker without the duck plus the weight of the duck itself.

Step 2: Evaluating Option B

Option B suggests that the weight of the beaker with the duck floating in it is less than the weight before adding the duck. This is also not true, as we have already mentioned that the duck displaces its own weight in water, and the beaker's weight after placing the duck would be equal to its initial weight plus the weight of the duck.

Step 3: Evaluating Option C

Option C suggests that the weight of the beaker with the duck floating in it is the same as the weight before adding the duck. This is the correct answer. According to Archimedes' Principle, a floating object displaces its own weight in the fluid it is floating in. So, the weight of the water spilled by the duck is equal to the weight of the duck. Thus, the weight before and after adding the duck remains the same.

Step 4: Evaluating Option D

Option D suggests that the weight of the beaker with the duck floating in it could be either greater or less than the weight before the duck was added, depending on the weight of the duck. This option is incorrect, as we have already established that the weight of the beaker will be the same before and after placing the duck, regardless of the duck's weight. In conclusion, the correct answer is: c) The weight of the beaker with the duck floating in it is the same as the weight before adding the duck.