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Classical unit conversion: determine how many dynes are equivalent to one newton (N).

Difficulty: Easy

Correct Answer: 105 dynes

Explanation:


Introduction / Context:
The dyne is a cgs unit of force; the newton is the S.I. unit. Conversions between these legacy and modern systems still appear in lab data, older texts, and entrance examinations. Knowing the power-of-ten factor is sufficient to convert quickly without a calculator.


Given Data / Assumptions:

  • 1 N is defined as 1 kg·m/s^2.
  • 1 dyne is defined as 1 g·cm/s^2.
  • 1 kg = 10^3 g; 1 m = 10^2 cm.


Concept / Approach:
Convert the S.I. definition into cgs base units using powers of ten for mass and length. The time unit (s) is common to both systems. Track exponents to compute the factor cleanly.


Step-by-Step Solution:

Start from 1 N = 1 kg·m/s^2.Replace kg with 10^3 g and m with 10^2 cm: 1 N = (10^3 g) * (10^2 cm) / s^2.Combine powers: 10^3 * 10^2 = 10^5, so 1 N = 10^5 g·cm/s^2.Recognize g·cm/s^2 as dyne → 1 N = 10^5 dynes.


Verification / Alternative check:

Reverse conversion: 1 dyne = 10^-5 N; multiplying by 10^5 returns 1 N.


Why Other Options Are Wrong:

10^4, 10^3, 10^2: understate the conversion by factors of 10–1000.10^6: overstates by 10.


Common Pitfalls:

Dropping a power-of-ten when converting metres to centimetres or kilograms to grams.Confusing dyne with newton-second (impulse) or other derived units.


Final Answer:

105 dynes
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