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JEE Main & Advanced Physics Elasticity Question Bank Rigidity Modulus

  • question_answer
    Two wires A and B of same length and of the same material have the respective radii \[{{r}_{1}}\] and \[{{r}_{2}}\]. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be [AIIMS 1980]

    A)                 \[\frac{r_{1}^{2}}{r_{2}^{2}}\]   

    B)                 \[\frac{r_{2}^{2}}{r_{1}^{2}}\]

    C)                 \[\frac{r_{2}^{4}}{r_{1}^{4}}\]   

    D)                 \[\frac{r_{1}^{4}}{r_{2}^{4}}\]

    Correct Answer: C

    Solution :

        Twisting couple \[C=\frac{\pi \eta {{r}^{4}}\theta }{2l}\] If material and length of the wires A and B are equal and equal twisting couple are applied then             \[\theta \propto \frac{1}{{{r}^{4}}}\] \ \[\frac{{{\theta }_{1}}}{{{\theta }_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{4}}\]


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