Answer:
0.701 mm.
Explanation:
From Hook's law,
Young modulus = Stress/Strain.
Stress = Force/area = F/A
Strain = ΔL/L.
Therefore,
γ = (F/A)/(ΔL/L)
γ = FL/ΔLA ...................... Equation 1
Where γ = Young's modulus, F = Force, L = Length of the pencil, ΔL = change in length of the pencil, A = cross sectional area.
Make ΔL the subject of the equation,
ΔL = FL/γA......................... Equation 2
But,
A = πd²/4......................... Equation 3
Where d = diameter
Substitute equation 3 into equation 2
ΔL = 4FL/γπd²................ Equation 4
Given: F = 4.9 N, L = 55 mm = 0.055 m, d = 0.7 mm = 0.0007 m, γ = 1×10⁹ N/m², π = 3.14.
Substitute into equation 4
ΔL = (4×4.9×0.055)/(1×10⁹×3.14×0.0007²)
ΔL = 1.078/1538.6
ΔL = 7.01×10⁻⁴ m.
ΔL = 0.701 mm.
