Railways Technical Ability Engineering Mechanics and Strength of Materials Question Bank Strength of Materials

  • question_answer A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be:

    A) k/4                               

    B) k/2

    C) 2k                                

    D) 4k

    Correct Answer: A

    Solution :

    \[{{n}_{1}}=N,\] \[{{D}_{1}}=D,\] \[{{d}_{1}}=d\,;\,\,{{d}_{2}}=d,\] \[{{G}_{1}}={{G}_{2}},\,{{n}_{2}}=N/2,\] \[{{D}_{2}}=2D\] Stiffness, k \[=\frac{D{{d}^{4}}}{8{{D}^{3}}n}\] For same G and d, \[k\propto \frac{1}{{{D}^{3}}n}\]             \[\frac{{{k}_{1}}}{{{k}_{2}}}={{\left( \frac{{{D}_{2}}}{{{D}_{1}}} \right)}^{3}}\times \left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)\] \[={{\left( \frac{2D}{D} \right)}^{3}}\times \left( \frac{N}{2N} \right)=4\] \[{{k}_{2}}=\frac{k}{4}\]

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