A 2-kg block displaces 10 kg of water when it is held fully immersed. The object is then tied down as shown in the figure; and it displaces 5 kg of water. What is the tension in the string?
A)10 N
B)20 N
C)30 N
D)70 N
E)100 N

Question

A 2-kg block displaces 10 kg of water when it is held fully immersed. The object is then tied down as shown in the figure; and it displaces 5 kg of water. What is the tension in the string? 
A)10 N 
B)20 N 
C)30 N 
D)70 N 
E)100 N

Quizplus · Accepted Answer

The buoyant force acting on the block is equal to the weight of water displaced by the block. Therefore, the initial buoyant force is equal to the weight of 10 kg of water, which is 10*9.8 = 98 N.

When the block is tied down, it can displace only 5 kg of water, which is equal to a buoyant force of 5*9.8 = 49 N.

The tension in the string is equal to the difference between the two buoyant forces, which is 98 - 49 = 49 N.

However, the question asks for the tension in the string, not the net force on the block. Therefore, the tension in the string is equal to the weight of the block minus the buoyant force when it displaces 5 kg of water.

The weight of the block is 2*9.8 = 19.6 N.

The buoyant force when it displaces 5 kg of water is 49 N.

Therefore, the tension in the string is 19.6 - 49 = -29.4 N.

But a negative tension does not make physical sense, therefore we take the magnitude of the tension, which is 29.4 N.

The closest choice is C) 30 N, which is the correct answer.

A 2-Kg Block Displaces 10 Kg of Water When It