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JEE Main & Advanced Sample Paper JEE Main Sample Paper-32

  • question_answer
    Wire A and B are connected with blocks P are as shown. The ratio of lengths, radii and Young?s modulus of wires A and B are r, 2r and 3r respectively (r is a constant). Find the mass of block P if ratio of increase in their corresponding lengths is \[1/6{{r}^{2}}\]. The mass of block Q is 3M.

    A) M           

    B)                   3M

    C) 6M      

    D)    9M

    Correct Answer: C

    Solution :

    \[\Delta l=\frac{FL}{AY}\] \[\frac{{{(\Delta l)}_{A}}}{{{(\Delta l)}_{B}}}=\frac{({{F}_{A}})}{({{F}_{B}})}\frac{({{L}_{A}})}{({{L}_{B}})}\frac{({{A}_{A}})}{({{A}_{B}})}\frac{({{Y}_{A}})}{({{Y}_{B}})}\] \[=\frac{(KM)}{(3M)}(r)\left( \frac{1}{2r} \right)\left( \frac{1}{3r} \right)=\frac{K}{36{{r}^{2}}}\] \[\frac{1}{6{{r}^{2}}}=\](given) K = 6 Mass of block P = 6 M


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