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JEE Main & Advanced Physics Wave Mechanics JEE PYQ-Wave Mechanics

  • question_answer
    Speed of transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross section\[1.0\,\,m{{m}^{2}}\]) is \[90\text{ }m{{s}^{1}}\]. If the Young’s modulus of wire is \[16\times {{10}^{11}}\text{ }N{{m}^{2}}\], the extension of wire over its natural length is: [JEE MAIN Held on 07-01-2020 Morning]

    A)  0.01 mm                     

    B)                                                                             0.02 mm

    C)  0.04 mm                     

    D)  0.03 mm

    Correct Answer: D

    Solution :

    (d)
    \[l=60\text{ }cm,\text{ }m=6\text{ }g,\text{ }A=1\text{ }m{{m}^{2}},\text{ }v=90\text{ }m/s\]
    \[v=\sqrt{\frac{T}{m}\times l}\Rightarrow T=\frac{m{{v}^{2}}}{l}\]
    \[\therefore \Delta L=\frac{Tl}{YA}=\frac{m{{v}^{2}}\times l}{l(YA)}\]
    \[=\frac{6\times {{10}^{-3}}\times {{90}^{2}}}{16\times {{10}^{11}}\times {{10}^{-6}}}=3\times {{10}^{-4}}m\]
    \[=0.03\,\,mm\]


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