When the tension in a metal wire is t1 and its length is l1. And when tension is t2 then length is l2 find the natural length of wire
Answers
The natural length of wire is I₁t₂ - l₂t₁ / (t₂ - t₁).
Explanation:
=> Suppose, the original length of the wire is L
According to the question,
=> For first situation, when the tension in a metal wire is t1 and its length is l1:
l1 = L + x₁
but as per the Hooke's Law, x = t/k
l₁ = L + t₁k₁
l₁ - L = t₁k₁ ... (1)
=> For second situation, when tension is t2 then length is l2:
l₂ = L + x₂
l₂ = L + (t₂/k)
l₂ - L = t₂/k ... (2)
=>By dividing eq(1) and (2), we get
l₁ - L/l₂ - L = t₁k / t₂k
l₁ - L/l₂ - L = t₁/ t₂
t₂ (l₁ - L) = t₁ (l₂ - L)
I₁t₂ - t₂L = l₂t₁ - t₁L
I₁t₂ - l₂t₁ = t₂L - t₁L
I₁t₂ - l₂t₁ = L (t₂ - t₁)
L = I₁t₂ - l₂t₁ / (t₂ - t₁)
Thus, the natural length of wire is I₁t₂ - l₂t₁ / (t₂ - t₁).
Learn more:
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