Speed of a transverse wave on a straight wire (mass 6.0g, length 60cm and area of cross-section 1.0m m ^ 2 is 90 ms ^ - 1 . If the Young's modulus of wire is 16 × 10 ^ 11 N m ^ - 2 , the extension of wire over its

Correct answer: A. 0.03mm v = (T)/(μ) ⇒ T = μ v ^ 2 ⇒ μ v ^ 2 A = Y(∆ l)/(l) ⇒ ∆ l = μ v ^ 2 l AY After substituting value of μ, v, l, A and Y we get ∆ l = 0 . 3mm

JEE Main 20207 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 7 January
Shift: Morning Shift
Subject: Physics
Chapter: Mechanical Properties of Solids

JEE Main 2020 · 7 January · Morning Shift · Physics · Mechanical Properties of Solids

Speed of a transverse wave on a straight wire (mass 6.0g, length...

Speed of a transverse wave on a straight wire (mass

6.0g,

length

60cm

and area of cross-section

1.0m{m}^{2}

90{ms}^{- 1}

. If the Young's modulus of wire is

16 \times {10}^{11}N{m}^{- 2}

, the extension of wire over its natural length is:

Options

A $0.03mm$
B $0.02mm$
C $0.04mm$
D $0.01mm$

Correct answer

A. $0.03mm$

Step-by-step solution

v = \sqrt{\dfrac{T}{\mu}}

⇒ T = \mu{v}^{2}

⇒ \dfrac{\mu{v}^{2}}{A} = Y\dfrac{∆ l}{l}

⇒ ∆ l = \dfrac{\mu{v}^{2}l}{AY}

After substituting value of

\mu, v, l, A

and

Y

we get

∆ l = 0 . 3mm

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