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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Mock Test - Gravitation and Mechanical Properties of Solid

  • question_answer
    Wires \[A\] and \[B\] are connected with blocks \[P\] and \[Q\], 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 \[\frac{1}{6{{r}^{2}}}\]. The mass of the block \[Q\] is 3\[M\]

    A) \[M\]               

    B) \[3M\]

    C) \[6M\]              

    D) \[9M\]

    Correct Answer: C

    Solution :

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


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