Question

If the atmospheric pressure is given by 10⁶ dyne/cm², the equivalent value in its SI unit will be-
1. 10⁶ N/m²
2. 10⁵ N/m²
3. 10⁴ N/m²
4. 10³ N/m²

Answer 1

Correct Answer - Option 2 : 10⁵ N/m²

The correct answer is option 2) i.e. 105 N/m2

CONCEPT:

• Système International (SI) unit is the metric system used for standard measurements of quantities.
  • It is also known as the MKS system.
  • This system considers metre (m) as the unit of length, kilogram (kg) as the unit of mass, and second (s) as the unit of time.
• CGS system considers centimetres (cm) as the unit of length, gram (g) as the unit of mass, and second (s) as the unit of time.

EXPLANATION:

• Dyne is the cgs unit for force. The SI unit of force is N.
• cm² is the cgs unit for the area. The SI unit for the area in m².
• Hence, the SI unit for atmospheric pressure is N/m².
• 1 dyne is equal to the force that would give a free mass of 1 g acceleration of 1 cm/s².

⇒ 1 dyne = 1 g × 1 cm/s²

⇒ 1 dyne = 10^-3 kg × 10^-2 m/s²  (∵ 1 m = 100 cm and 1 kg = 1000 g)

⇒ 1 dyne = 10^-5 N

⇒ 106 dyne/cm2 = \(\frac{10^{6} \times 10^{-5}N}{(10^{-2})^2m^2} = 10^5 \:N/m^2\)