Question

Fill in the blank.
The loss of weight of an object that is immersed in water is numerically equal to the _ _ _ _.
A. Buoyant force
B. Density of the body
C. Volume of the body
D. Volume of the liquid

Answer 1

Hint: Recall Archimedes principle. Archimedes’s principle states that an object partially or completely submerged in the liquid experiences an upward force equal to the weight of the liquid displaced by the object. Also, the loss in the weight of the object when submerged in the water is equal to the weight of the liquid displaced by the object.

Complete answer:
This question is based on Archimedes’s principle. Let’s recall Archimedes’s principle which states that an object partially or completely submerged in the liquid experiences an upward force equals to the weight of the liquid displaced by the object. The upward force is known as buoyant force. When we submerge the object in the water it’s the apparent weight decreases. This loss in the weight of the object is equal to the weight of the liquid displaced by the body.

According to Archimedes’s principle, we have seen that the loss in the weight of the object when submerged in the water is equal to the weight of the liquid displaced by the object. But the weight of the liquid displaced by the body is the buoyant force exerted by the liquid on the object. Therefore, the correct answer is option (A).

The expression for the buoyant force is,
\[{F_b} = \rho gV\]
Here, \[\rho \] is the density of the liquid, g is the acceleration due to gravity and V is the volume of the displaced liquid.

The loss of weight of an object that is immersed in water cannot be equal to the density or volume of water or object since the dimensions of weight and density or weight and volume are different. Therefore, the rest of the options are incorrect.

So, the correct answer is option A.

Note:The other way to answer this question is to compare the dimensional units of weight with the units of given options. The dimension of weight has unit of force, therefore, only the buoyant force can be equal to the loss in the weight. The unit of density is \[{\text{kg/}}{{\text{m}}^3}\] and unit of volume is \[{{\text{m}}^{\text{3}}}\].