The apparent weight of the body in a liquid is

A) V(ρ - ρL)g

B) Vρg

C) VρLg

D) None of these.

To determine the apparent weight of a body submerged in a liquid, we need to consider the principles of buoyancy and how they affect the weight of the object. The apparent weight is essentially the weight of the object minus the buoyant force acting on it. Let's break this down step by step.

Understanding Buoyancy

When an object is submerged in a fluid, it experiences an upward force known as the buoyant force. This force is equal to the weight of the fluid displaced by the object, which can be calculated using Archimedes' principle. The formula for buoyant force (F_b) is:

• F_b = V * ρ_L * g

Where:

• V = volume of the submerged part of the object
• ρ_L = density of the liquid
• g = acceleration due to gravity

Calculating Apparent Weight

The actual weight (W) of the object in air can be expressed as:

• W = V * ρ * g

Where:

• ρ = density of the object

The apparent weight (W_a) of the object when submerged in the liquid is given by the formula:

• W_a = W - F_b

Substituting the expressions for weight and buoyant force, we get:

• W_a = (V * ρ * g) - (V * ρ_L * g)

This simplifies to:

• W_a = V * g * (ρ - ρ_L)

Final Expression for Apparent Weight

From the derived formula, we can see that the apparent weight of the body in a liquid is:

• W_a = V(ρ - ρ_L)g

Thus, the correct answer to your question is:

• A) V(ρ - ρ_L)g

Real-World Application

This concept is crucial in various fields, such as engineering and fluid mechanics. For example, when designing ships or submarines, understanding how buoyancy affects weight is essential for stability and performance. Similarly, in medical applications, the buoyancy of human organs in fluids can influence surgical procedures and diagnostics.

In summary, the apparent weight of an object submerged in a liquid is influenced by both its own density and the density of the liquid, leading us to the conclusion that the correct formula is indeed A) V(ρ - ρ_L)g.