Question

One newton is equal to_____

• A. \(10^2 \text{ dyne}\)
• B. \(10^4 \text{ dyne}\)
• C. \(10^7 \text{ dyne}\)
• D. \(10^5 \text{ dyne}\)

Hint:

A simple memory rule: the power of 10 is the sum of the powers of the conversions:
- Mass: \(\text{kg} \rightarrow \text{g}\) is \(10^3\)
- Length: \(\text{m} \rightarrow \text{cm}\) is \(10^2\)
Sum of exponents: \(3 + 2 = 5 \implies 10^5\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Newton (\(\text{N}\)) is the SI unit of force, while the dyne is the CGS (Centimetre-Gram-Second) unit of force.
To find the relationship between them, we convert the fundamental base units of the SI system to CGS base units.

Step 2: Detailed Explanation:
The definition of force from Newton's second law is:
\[ \text{Force} = \text{Mass} \times \text{Acceleration} \]
In the SI system:
\[ 1 \text{ Newton (N)} = 1 \text{ kg} \cdot \text{m/s}^2 \]
In the CGS system:
\[ 1 \text{ dyne} = 1 \text{ g} \cdot \text{cm/s}^2 \]
Let us convert kilograms to grams and meters to centimeters:
\[ 1 \text{ kg} = 10^3 \text{ g} \]
\[ 1 \text{ m} = 10^2 \text{ cm} \]
Substitute these conversion factors into the expression for one Newton:
\[ 1 \text{ N} = (10^3 \text{ g}) \cdot \left(\frac{10^2 \text{ cm}}{\text{s}^2}\right) \]
Combine the powers of 10:
\[ 1 \text{ N} = 10^3 \cdot 10^2 \left(\text{g} \cdot \text{cm/s}^2\right) \]
\[ 1 \text{ N} = 10^5 \text{ dyne} \]
This matches Option D.

Step 3: Final Answer:
One newton is equal to \(10^5 \text{ dyne}\).