Question

A body floats in a liquid contained in a beaker. The whole system as shown in the figure falls freely under gravity. The upthrust on the body is

A. Zero
B. equal to the weight of the liquid displaced.
C. equal to the weight of the body in air
D. equal to the weight of the immersed portion of the body

Answer 1

When an object enters water, it is subjected to two forces: a downward force known as gravity, which is an invisible force that pulls objects together, and an upward force known as buoyancy, which is an upthrust imposed by a fluid that opposes the weight of a partially or completely submerged object.

Complete answer:
A. When the beaker is permitted to fall naturally, the body's visible weight becomes zero, implying that the body exerts no impact on the water. As a result, no water is displaced because of the body's weight. Therefore, the buoyant force, or upthrust, would be zero.Hence, this option is correct.

B. The weight of the body is equal to the weight of the liquid displaced only when the total upward force (buoyant force) is equal to the total downward force in a floating vessel. In this case, the body will be in equilibrium and it will float in water. But in this question, the object remains suspended in water. Hence, this option is incorrect.

C. In the air the weight is proportional to the product of its mass and acceleration due to gravity. However, when a body is submerged in water, it is subjected to an upthrust force, which acts opposite to the weight force. As a result, the weight of the body in air is greater than the weight of the body in water. Hence, this option is incorrect as the weights cannot be equal.

D. The weight of the body immersed is equal to the weight of the liquid displaced. It remains the same for both partial or complete immersing. Now, this condition holds true when the object is floating. But in this case, the object remains suspended. Hence, this option is incorrect.

Therefore, the correct option is A.

Note: Few real-life applications of buoyant force are as follows: Submarines submerge by releasing water into their ballast tanks, causing their weight to exceed the buoyant force. The atmosphere is packed with air, which gives every object a buoyant energy. Due to the buoyant power, a hot air balloon rises and floats (when the surrounding air is greater than its weight).