Question

1 Newton = ____ Dyne.

• A. \(10^5\)
• B. \(10^4\)
• C. \(10^3\)
• D. \(10^2\)

Hint:

1 Newton = (1 kg) \(\times\) (1 m/s\(^2\)). 1 Dyne = (1 g) \(\times\) (1 cm/s\(^2\)). Convert kg to g and m to cm: \(1 \text{ kg} = 1000 \text{ g} = 10^3 \text{ g}\) \(1 \text{ m} = 100 \text{ cm} = 10^2 \text{ cm}\) So, 1 Newton = \((10^3 \text{ g}) \times (10^2 \text{ cm/s}^2)\) 1 Newton = \(10^3 \times 10^2 \text{ (g} \cdot \text{cm/s}^2)\) 1 Newton = \(10^5 \text{ Dyne}\).

Answer 1

The Correct Option is A

Concept: The Newton (N) is the SI unit of force. The Dyne is the CGS (Centimeter-Gram-Second) unit of force. We need to find the conversion factor between them. Force is defined by Newton's second law: \(F = ma\) (Force = mass \(\times\) acceleration). Step 1: Define 1 Newton in terms of base SI units In the SI system:
Mass (\(m\)) is measured in kilograms (kg).
Acceleration (\(a\)) is measured in meters per second squared (\(\text{m/s}^2\)). So, \(1 \text{ Newton (N)} = 1 \text{ kg} \cdot \text{m/s}^2\). Step 2: Define 1 Dyne in terms of base CGS units In the CGS system:
Mass (\(m\)) is measured in grams (g).
Acceleration (\(a\)) is measured in centimeters per second squared (\(\text{cm/s}^2\)). So, \(1 \text{ Dyne} = 1 \text{ g} \cdot \text{cm/s}^2\). Step 3: Convert kilograms to grams and meters to centimeters We know:
\(1 \text{ kg} = 1000 \text{ g} = 10^3 \text{ g}\)
\(1 \text{ m} = 100 \text{ cm} = 10^2 \text{ cm}\) Step 4: Express 1 Newton in CGS units Substitute the conversions from Step 3 into the definition of 1 Newton from Step 1: \[ 1 \text{ N} = (1 \text{ kg}) \times (1 \text{ m/s}^2) \] \[ 1 \text{ N} = (10^3 \text{ g}) \times (10^2 \text{ cm/s}^2) \] \[ 1 \text{ N} = 10^3 \times 10^2 \text{ (g} \cdot \text{cm/s}^2) \] \[ 1 \text{ N} = 10^{(3+2)} \text{ g} \cdot \text{cm/s}^2 \] \[ 1 \text{ N} = 10^5 \text{ g} \cdot \text{cm/s}^2 \] Since \(1 \text{ Dyne} = 1 \text{ g} \cdot \text{cm/s}^2\), we have: \[ 1 \text{ N} = 10^5 \text{ Dyne} \] Therefore, 1 Newton is equal to \(10^5\) Dynes. This matches option (1).