Answer:
0.8895m
Explanation:
Cable diameter = 0.0125m
Mass of elevator = 6450kg
Young Modulus(E) = 2.11*10¹¹N/m
∇l (change in length) =
L = 362m
A = Πr², but r = d / 2 = 0.0125 / 2 = 0.00625m
A = 3.142 * (0.00625)² = 1.227*10^-4m²
Young Modulus (E) = Tensile stress / Tensile strain
E = (F / A) / ∇l / L
F = mg = 6450 * 9.8 = 63210N
2.11*10¹¹ = (63210 / 1.22*10^-4) / (∇l / 362)
2.11*10¹¹ = 5.18*10⁸ / (∇l / 362)
2.11*10¹¹ = (5.18*10⁸ * 362) / ∇l
2.11*10¹¹ = 1.875*10¹¹ / ∇l
∇l = 1.875*10¹¹ / 2.11*10¹¹
∇l = 0.8895m
The change in length is 0.8895m
Answer:
The length of rod A will be <u>greater than </u>the length of rod B
Explanation:
We, know that the formula for final length in linear thermal expansion of a rod is:
L' = L(1 + ∝ΔT)
where,
L' = Final Length
L = Initial Length
∝ = Co-efficient of linear expansion
ΔT = Change in temperature
Since, the rods here have same original length and the temperature difference is same as well. Therefore, the final length will only depend upon the coefficient of linear expansion.
For Rod A:
∝₁ = 12 x 10⁻⁶ °C⁻¹
For Rod B:
∝₂ = β₂/3
where,
β₂ = Coefficient of volumetric expansion for rod B = 24 x 10⁻⁶ °C⁻¹
Therefore,
∝₂ = 24 x 10⁻⁶ °C⁻¹/3
∝₂ = 8 x 10⁻⁶ °C⁻¹
Since,
∝₁ > ∝₂
Therefore,
L₁ > L₂
So, the length of rod A will be <u>greater than </u>the length of rod B
