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JEE Main & Advanced Physics Elasticity Question Bank Youngs Modulus and Breaking Stress

  • question_answer
    A rubber cord catapult has cross-sectional area \[25m{{m}^{2}}\]and initial length of rubber cord is \[10cm.\] It is stretched to \[5\,cm.\] and then released to project a missile of mass \[5gm.\] Taking \[{{Y}_{rubber}}=5\times {{10}^{8}}N/{{m}^{2}}\] velocity of projected missile is                        [CPMT 2002]

    A)             \[20\,m{{s}^{-1}}\]

    B)                      \[100\,m{{s}^{-1}}\]

    C)             \[250\,m{{s}^{-1}}\]

    D)                      \[200\,m{{s}^{-1}}\]

    Correct Answer: C

    Solution :

                    Potential energy stored in the rubber cord catapult will be converted into kinetic energy of mass. \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}\frac{YA{{l}^{2}}}{L}\]Þ \[v=\sqrt{\frac{YA{{l}^{2}}}{mL}}\]             \[=\sqrt{\frac{5\times {{10}^{8}}\times 25\times {{10}^{-6}}\times {{(5\times {{10}^{-2}})}^{2}}}{5\times {{10}^{-3}}\times 10\times {{10}^{-2}}}}=250\ m/s\]


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