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

  • question_answer
    Two rods A and B of the same material and length have their radii \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio \[\left( \frac{Angle\,of\,twist\,at\,the\,end\,of\,A}{Angle\,of\,twist\,at\,the\,end\,of\,B} \right)\]

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

    B) \[r_{1}^{3}/r_{2}^{3}\]

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

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

    Correct Answer: C

    Solution :

    [c] Couple per unit angle of twist, \[C=\frac{\pi \eta {{r}^{4}}}{2\ell }\] \[\therefore \,\,\,\,Couple\,\,\tau =C\theta =\frac{\pi \eta {{r}^{4}}\theta }{2\ell }\] Here \[\eta \], \[\ell \], C & \[\tau \] are same. So, \[{{r}^{4}}\theta =\]constant \[\therefore \,\,\,\frac{{{\theta }_{1}}}{{{\theta }_{2}}}=\left( \frac{r_{2}^{4}}{r_{1}^{4}} \right)\]


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