Two identical beakers are filled with the same amount of water. A ball of mass m is placed in the first beaker so that it floats on the surface while a second identical ball is placed in the second beaker but tied with a string of negligible mass so that the ball is completely submerged. Each beaker is then placed on a scale. Which scale has a higher reading?
A) a
B) b
C) the same
D) depends on how deep the ball is submerged in b
E) depends on the mass of the ball

Question

Two identical beakers are filled with the same amount of water. A ball of mass m is placed in the first beaker so that it floats on the surface while a second identical ball is placed in the second beaker but tied with a string of negligible mass so that the ball is completely submerged. Each beaker is then placed on a scale. Which scale has a higher reading?
A) a 
B) b 
C) the same 
D) depends on how deep the ball is submerged in b 
E) depends on the mass of the ball

Quizplus · Accepted Answer

Both the balls displace the same amount of water, which is equal to the weight of the water they replace. Since the amount of water displaced is the same in both beakers, the reading on the scales will be the same. The weight of the balls does not affect the reading on the scales as gravity acts on them equally in both cases. Similarly, the depth to which the ball is submerged does not affect the weight of the displaced water and hence does not affect the reading on the scales.

Two Identical Beakers Are Filled with the Same Amount of Water