Problem 31 - Master Resource Book in JEE Main Physics

Question

One yard in SI unit is equal (a) \(1.9144 \mathrm{~m}\) (b) \(0.9144 \mathrm{~m}\) (c) \(0.09144 \mathrm{~km}\) (d) \(1.0936 \mathrm{~km}\)

Step-by-Step Solution

Answer

Option (b) is correct: 0.9144 m.

Step 1: Understanding the Problem

The problem provides four different values for one yard in International System of Units (SI unit), which is meters (m) or kilometers (km), and asks to identify the correct conversion.

Step 2: Recall Yard Conversion

Recall that 1 yard is defined as exactly 0.9144 meters in the SI unit system. This is a standard conversion factor used universally.

Step 3: Compare with Given Options

Compare the standard conversion value of 0.9144 meters with the options provided. Option (b) directly matches the standard conversion value: 0.9144 meters.

Key Concepts

Yard to Meter Conversion

Converting yards to meters is an essential part of understanding measurement systems, especially when working with international data or traveling. A yard is a unit of length in the customary system primarily used in the United States and the United Kingdom. In contrast, a meter is part of the International System of Units, also known as SI units, which are widely used worldwide. To convert yards into meters, a specific conversion factor is applied. Knowing this conversion is crucial for many applications, from construction to travel.

The standard conversion for one yard to meters is:

• 1 yard = 0.9144 meters

This means that every yard can be directly translated into 0.9144 of a meter. So, if you are given a measurement in yards and need it in meters, simply multiply the yard value by 0.9144. This conversion helps maintain uniformity and precision across various platforms involving measurements, such as scientific endeavors or cross-border engineering projects.

SI Units

The International System of Units (SI) is the modern form of the metric system. It is the most widely used system of measurement for science, industry, and trade worldwide. SI units aim to offer consistency and uniformity across different fields and regions, thus reducing confusion caused by multiple measurement systems.

Key features of the SI system include:

• Base units such as meters, kilograms, and seconds, which are used to derive other units.
• Derived units, which are combinations of base units, like meters per second for speed.
• International consensus and adoption, facilitating global communication and collaboration.

Use of SI units ensures that scientists and professionals can share and compare information reliably and accurately. It provides a universal language of measurement that eliminates the need for conversion, except when interacting with non-metric systems.

Standard Conversion Factor

A standard conversion factor is a constant number used to convert a quantity from one unit to another. Such factors are crucial as they allow for accurate and reliable conversions between different measurement systems. In our context, it refers to the consistent number used for changing yards into meters, which is 0.9144.

This factor is fixed and universally accepted, meaning it doesn't change regardless of the circumstances or application. Conversion factors are derived from precise measurements and are maintained by international standards organizations to ensure consistency and accuracy.

Using standard conversion factors:

• Ensures precision by reducing human error in manual conversions.
• Simplifies calculations, especially in fields requiring rapid and frequent conversions.
• Supports collaboration across different regions and industries.

For any conversion task, recalling the correct standard conversion factor is key. It is particularly essential when dealing with complex systems where multiple units might interact.