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Q.

Speed of transverse wave on a straight wire (mass 6.0g, length 60cm and area of cross section 1.0 $m m^{2}$ ) is 90 $m s^{- 1}$ . If the young’s modulus of wire in $16 \times 10^{11} N m^{- 2}$ the extension of wire over its natural length is.

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a

0.01mm

b

0.02mm

c

0.04mm

d

0.03mm

answer is A.

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Detailed Solution

$\begin{array}{l} S p e e d o f T r a n s v e r s e W a v e, V = \sqrt{\frac{T}{μ}} h e r e T = T e n s i o n a n d μ = L i n e a r m a s s d e n s i t y \\ \Rightarrow T = μ v^{2} \\ \Rightarrow \frac{μ V^{2}}{A} = Y \frac{Δ l}{l} [∵ Y = \frac{\frac{T}{A}}{\frac{Δ l}{l}}] \\ \Rightarrow Δ l = \frac{μ V^{2} l}{A Y} \\ \Rightarrow Δ l = \frac{6 \times 10^{- 3} \times 90 \times 90}{1 \times 10^{- 6} \times 16 \times 10^{11}} = 0.03 m m \end{array}$

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