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JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Mechanical Properties of Solids

  • question_answer
    A body of mass 10 kg is attached to a wire of radius 3 cm. Its breaking stress is\[4.8\times {{10}^{7}}N{{m}^{-2}}\], the area of cross-section of the wire is\[{{10}^{-6}}{{m}^{2}}\] . What is the maximum angular velocity with which it can be rotated in the horizontal circle?

    A) \[1\,rad{{\sec }^{-1}}\]

    B) \[2\,rad{{\sec }^{-1}}\]

    C) \[4\,rad{{\sec }^{-1}}\]

    D) \[8\,rad{{\sec }^{-1}}\]

    Correct Answer: C

    Solution :

    [c] Given that F/A = \[4.8\times {{10}^{7}}N{{m}^{-2}}\] \[\therefore \,\,F=4.8\times {{10}^{7}}\times A\] or  \[\frac{m{{v}^{2}}}{r}=4.8\times {{10}^{7}}\times {{10}^{-6}}=48\] or \[\frac{m{{r}^{2}}{{\omega }^{2}}}{r}=48\,\,or\,\,{{\omega }^{2}}=\frac{48}{mr}\] \[\omega =\sqrt{\left( \frac{48}{10\times 0.3} \right)=}\sqrt{16}=4rad/\sec \]


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