Problem 71 - Master Resource Book in JEE Main Physics

Question

If \(g_{E}\) and \(g_{M}\) are the acceleration due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on two surfaces, one will find the ratio electronic charge on the moon electronic charge on the earth to be (a) \(g_{m} / g_{E}\) (b) 1 (c) 0 (d) \(g_{E} / g_{M}\)

Step-by-Step Solution

Answer

Option (b) 1.

Step 1: Define key parameters

Let's identify the expressions we need. The acceleration due to gravity on Earth is denoted by \(g_{E}\), and on the Moon by \(g_{M}\). We are asked to find the ratio of electronic charges based on these gravitational accelerations.

Step 2: Understand Millikan's oil drop experiment

Millikan's experiment is designed to measure the elementary charge by balancing gravitational and electric forces. The electronic charge is not dependent on the gravitational field where the experiment is performed.

Step 3: Analyze the ratio

Since the electronic charge is a fundamental constant (i.e., it doesn't change whether you're on the Earth or the Moon), the ratio of the electronic charge on the Moon to that on the Earth is independent of gravitational acceleration. Thus, this ratio is \(1\).

Step 4: Choose the correct option

The ratio of the electronic charge on the Moon to the electronic charge on the Earth, based on Millikan's experiment, is \(1\). Therefore, the correct answer among the options given is (b) 1.

Key Concepts

Electronic Charge

The concept of electronic charge is crucial in understanding electrical phenomena. The electronic charge is the charge carried by a single electron, and it is denoted by the symbol \(e\). It is a fundamental property, meaning it does not change regardless of the environment. Whether you are on Earth or the Moon, the electronic charge remains constant. This concept is central to experiments like Millikan's oil drop experiment, where scientists aim to measure the elementary charge with great precision. The fixed nature of the electronic charge is why it remains unaffected by external factors such as gravity.

• Constant value, independent of location
• Measured in coulombs (C)
• Essential for understanding the nature of electric forces

Acceleration Due to Gravity

Acceleration due to gravity refers to the force that attracts objects toward the center of a massive body like Earth or the Moon. On Earth, this value is approximately \(9.8 \, \text{m/s}^2\) and is denoted as \(g_E\). The Moon has a much weaker gravitational pull, with an acceleration value of \(g_M\).
This difference is due to the Moon's smaller mass and size compared to Earth. Despite this variance, the acceleration due to gravity does not affect the fundamental properties of particles, such as electronic charge. When performing Millikan's oil drop experiment in different gravitational fields, the fundamental charge remains the same, highlighting the independence of electronic charge from gravitational factors.

Gravitational Forces

Gravitational forces are the attraction between two masses, such as an object and a planet. This force is strongest when the masses are larger and closer together. It acts at a distance, which means that even if two objects are not touching, they can still exert a gravitational pull on each other.
In Millikan's oil drop experiment, gravitational forces are balanced with electrical forces to measure the electronic charge of a droplet. By knowing the gravitational pull on the drop, scientists can accurately compute the elementary charge by compensating with an electric field.

• Depends on mass and distance
• Affects how objects fall, but not the intrinsic charge
• Used to balance forces in precision experiments

Elementary Charge

The elementary charge is a fundamental concept in physics, representing the smallest unit of electric charge that is considered indivisible in classical terms. The magnitude of the elementary charge is approximately \( 1.602 \times 10^{-19} \text{C}\). It is the charge of a single proton (or the opposite of an electron), which helps in identifying and quantifying the behavior of charged particles.
In Millikan's oil drop experiment, this charge is measured by observing tiny droplets suspended between two electric plates. By adjusting the voltage across the plates, the forces on the droplets can be balanced, allowing scientists to calculate the elementary charge precisely. Understanding the elementary charge is foundational for diving into deeper topics in electromagnetism and quantum physics.

• A basic unit of charge
• Measured using experiments like Millikan's
• Invariable and universal constant