Problem 61 - Master Resource Book in JEE Main Physics

Question

A body floats in a liquid contained in a beaker. If the whole system falls under gravity, then the upthrust on the body due to liquid is IUP SEE 2009] (a) equal to the weight of the body in air (b) equal to the weight of the body in liquid (c) zero (d) equal to the weight of the immersed part of the body

Step-by-Step Solution

Answer

(c) zero

Step 1: Understanding the Problem

A body floating in a liquid experiences an upward force, known as upthrust. We are asked to determine how this upthrust changes if the whole system, consisting of the beaker, liquid, and floating body, is in free fall under gravity.

Step 2: Analyze Free Fall Conditions

When the entire system falls under gravity, it is in a state of free fall. In free fall, the apparent gravitational force acting on all components of the system is zero. This is because every part, including the liquid and the body, accelerates downwards with the acceleration due to gravity.

Step 3: Effect on Upthrust Force

The upthrust or buoyant force is due to the pressure difference between the top and bottom of the submerged part of the body in the fluid. In free fall, since there is no effective gravitational force acting on the liquid, the pressure difference that creates the upthrust becomes zero.

Step 4: Conclusion on Upthrust

With the apparent gravitational force being zero in free fall, the upthrust also decreases to zero. The floating body's behavior changes because both it and the liquid fall together without any relative difference in pressure.

Key Concepts

Buoyant Force

Buoyant force, also known as upthrust, is a crucial concept in physics, especially when dealing with fluids. It is the upward force that a fluid exerts on an object immersed in it. This force occurs due to the pressure differences between the top and the bottom of the object. The larger pressure at the bottom results in a net upward force.

• It can be observed when objects float, sink, or hover in a fluid.
• The magnitude of the buoyant force equals the weight of the fluid displaced by the object, as per Archimedes' principle.

In our exercise, when the system is at rest, the body floating in the liquid experiences this upward force. However, the scenario changes once the system is in free fall, affecting the conditions for this force.

Gravitational Force

Gravitational force is the attractive force that the Earth exerts on objects. It pulls objects towards the center of the Earth and is responsible for the weight that we feel.

• This force is proportional to the mass of the object and the gravitational acceleration, expressed as\[ F = m \times g \]
• Where \( F \) is the gravitational force, \( m \) is the mass, and \( g \) is the gravitational acceleration (approximately \( 9.81 \, m/s^2 \)).

In the context of this exercise, when the entire system is in free fall, the gravitational force is still acting, but its effect is neutralized because the whole system accelerates downward at the same rate.

Free Fall Physics

Free fall is a fascinating part of physics where an entire system, or object, is under the influence of gravity alone. In such scenarios, other forces like air resistance are negligible or absent.

• During free fall, objects experience weightlessness because they are accelerating downwards at the same rate as the gravitational pull.
• This results in the apparent gravitational force being effectively zero within the system.

For the floating body in our exercise, this means that the conditions that result in buoyant force are altered drastically, as both the liquid and the floating body experience the same gravitational pull and acceleration.

Pressure Differences

Pressure differences are at the heart of understanding buoyant forces. In a fluid, pressure exerted increases with depth due to the weight of the liquid above.

• This is why the bottom part of a submerged object in a fluid experiences higher pressure compared to the top, generating a net upward force.
• The equation for pressure in a fluid is given by \[ P = \rho \times g \times h \]
• Where \( P \) is pressure, \( \rho \) is fluid density, \( g \) is gravitational acceleration, and \( h \) is height or depth in the fluid.

In free fall, however, as gravity's effect is neutralized, these pressure differences disappear, effectively eliminating the buoyant force.

Floating Body Mechanics

Floating body mechanics involves the interaction between an object and the fluid it is in, dictating whether it floats or sinks.

• For an object to float, the buoyant force must equal the gravitational force pulling it down.
• Conditions like density of the body versus the fluid play a significant role in determining floating stability.

In our exercise, during free fall, the mechanics change drastically. The concept of buoyancy becomes irrelevant as both the body and the fluid interact in a manner where pressure differences do not exist, making the body float with the same motion as the liquid.