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

  • question_answer A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness k. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will be:

    A) k                                  

    B) 1.25 k

    C) 1.56 k              

    D) 1.95 k

    Correct Answer: C

    Solution :

    d=10 mm, \[{{n}_{1}}=8,\] \[{{D}_{ml}}=75\,mm\] \[{{n}_{2}}=10,\] \[{{D}_{m2}}=60\,mm\] Spring stiffness, \[k=\frac{G{{d}^{4}}}{8D_{m}^{3}n}\] \[\therefore \,\,k\propto \frac{1}{D_{m}^{3}n}\] \[\frac{{{k}_{2}}}{{{k}_{1}}}=\frac{D_{m1}^{3}{{n}_{1}}}{D_{m2}^{3}{{n}_{2}}}={{\left( \frac{75}{60} \right)}^{3}}\times \frac{8}{10}\] \[{{k}_{2}}=1.5625\,\,k\]

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