a string of cross section 2 cm^2 is doubled in length by the application of a longitudinal force 2*10^5dynes.the young"s modulus is:
1.10^5 dyne/cm^2
To find the Young's modulus, we need to use the formula:
Young's modulus (Y) = Stress / Strain
In this case, we are given the force applied (F) and the change in length (ΔL). Stress is defined as the force per unit area, while strain is defined as the change in length per unit original length. Using the formula for stress and strain, we can calculate Young's modulus.
Given:
- Force (F) = 2 * 10^5 dynes
- Change in length (ΔL) = original length (L)
- Cross-sectional area (A) = 2 cm^2
Step 1: Convert area from cm^2 to cm^2
Since the given area is already in cm^2, no conversion is necessary.
Step 2: Calculate the stress
Stress (σ) = Force (F) / Area (A)
Substituting the given values:
σ = (2 * 10^5 dynes) / (2 cm^2)
Step 3: Simplify the expression
σ = 1 * 10^5 dynes/cm^2
Step 4: Calculate the strain
Strain (ε) = Change in length (ΔL) / Original length (L)
Given that the change in length is equal to the original length (L), the strain can be written as:
ε = L / L
Step 5: Simplify the expression
ε = 1
Step 6: Calculate Young's modulus
Young's modulus (Y) = Stress (σ) / Strain (ε)
Substituting the calculated stress and strain:
Y = (1 * 10^5 dynes/cm^2) / 1
Step 7: Simplify the expression
Y = 1 * 10^5 dynes/cm^2
Therefore, the Young's modulus is 1 * 10^5 dyne/cm^2.
a string of cross section 2 cm^2 is doubled in length by the application of a longitudinal force 2*10^5dynes.the young"s modulus is:
1.10^5 dyne/cm^2