Question

Young’s modulus of steel is 19× 1010 N/m2. Express it in dynes cm2. Here dynes are the C.G.S unit of force.

CLASS - XI PHYSICS (Physical World & Measurement)

Answer 1

1N = 100000 dynes = 10⁵ dynes
1m² = 10000 cm² = 10⁴ cm²

1N/m² = 10⁹ dynes/cm²
So 19×10¹° N/m² = 19×10¹°×10⁹ = 1.9×10²°dynes/cm²

Answer 2

Answer:

Youngs modulus of steel in dyne/$\bold{\mathrm{cm}^{2}}$ is $\bold{19 \times 10^{11} \mathrm{dyne} / \mathrm{cm}^{2}}$

Explanation:

Dyne and Newton, both are units of force. While Dyne is specified in C-G-S(Centimeter – Gram – Second) unit system, Newton is specified in modern SI unit system which gives the relationship Young’s Modulus between stress and strain. It is used to measure hardness of material.

Here stress is force applied per unit area, strain is deformation happened on object.

$\mathrm{E}=\mathrm{G} / \epsilon=F / A / \Delta L / L o=\mathrm{Flo} / \mathrm{A} \Delta L$

Where, $\sigma$ = Stress in Pascal

ϵ = Strain or deformation

F = Force

A = Cross sectioned area

∆L = Change in Length

Lo = Actual Length

E = Young’s Modulus

Here E =  $19 \times 10^{10} \mathrm{N} / \mathrm{m}^{2}$

We know that 1 Newton = $\bold{10^{5}}$ dyne

Explanation of how 1 Newton = $10^{5}$ dyne is as follows:

Converting $\left[\mathrm{Kg} \times \mathrm{m} / \mathrm{S}^{2}\right] \rightarrow\left[\mathrm{g} \times \mathrm{cm} / \mathrm{S}^{2}\right]$

$=(1000 \mathrm{gm}) \times(100 \mathrm{cm}) / 1 \text { Second }^{2}=10^{5} \mathrm{gm} \times \mathrm{cm} / \mathrm{S}^{2}=10^{5}$ dyne

So Now E $=19 \times 10 \stackrel{10}{m} \mathrm{N} / \mathrm{m}^{2}=19 \times 10^{10}\left(10^{5}\right) \text { dyne / }(100)^{2} \mathrm{cm}^{2}$

$\bold{\mathrm{E}=19 \times 10^{11} \mathrm{dyne} / \mathrm{cm}^{2}}$