Three balls are in water


Asked by maham237 @ in Physics viewed by 383 People


Three balls are in water. Ball 1 floats, with half of it exposed above the water level. Ball 2, with a density less than the density of water is held below the surface by a cord anchored to the bottom of the container, so that it is fully submerged. Ball 3, of same radius as ball 2, but of greater mass, is suspended from a rope so that it is fully submerged.Part (a) Which is true for Ball 1? Choose the best answer. a. The magnitude of the buoyancy force is less than that of the ball's weight. b. The magnitude of the buoyancy force is equal to that of the ball's weight. c. The magnitude of the buoyancy force is more than that of the ball's weight. d. The magnitude of the buoyancy force is exactly one half of that of the ball's weight. Part (b) Which is true for Ball 2? Choose the best answer. a.The magnitude of the buoyancy force is less than that of the ball's weight. b.The magnitude of the buoyancy force is larger than that of the ball's weight. c. The magnitude of the buoyancy force is equal to that of the ball's weight. d. The magnitude of the buoyancy force is exactly one half of that of the ball's weight. Part (c) Consider Ball 2 and Ball 3. Which one experiences the larger buoyancy force? Choose the best answer a. Ball 2 b. They both have the same buoyancy force. c. The answer depends on the forces in the ropes. d. Ball 3

Answered by maham237 @



Answer:

(a) Option B

The magnitude of the buoyancy force is equal to that of the ball's weight.

(b) Option B

The magnitude of the buoyancy force is larger than that of the ball's weight.

(c) Option B

They both have the same buoyancy force.

Explanation:

(a)

Ball 1

The sum of vertical forces is zero hence F_{ynet}=0 therefore

B-mg=0 where B is buoyancy force, m is mass of ball, g is acceleration due to gravity

B=mg

mg is weight of ball

Therefore, option B, The magnitude of the buoyancy force is equal to that of the ball's weight


(b)


Ball 2

The sum of vertical forces is zero hence F_{ynet}=0 therefore

B-T-mg=0 where B is buoyancy force, m is mass of ball, g is acceleration due to gravity and T is tension in the string

B=mg+T

Therefore, option B, The magnitude of the buoyancy force is larger than that of the ball's weight.

(c
)

Ball 2 and 3

They have similar buoyancy force since the weight displaced by the body equals the buoyancy force. In this case, the weight of the displaced fluid is proportional to the volume of the ball since the two balls have same volume. It therefore means that their buoyancy forces are also the same.


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