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Railways NTPC (Technical Ability) Engineering Mechanics and Strength of Materials Question Bank Engineering Mechanics

  • question_answer
           Two closed-coil springs are made from the same small diameter wire, one wound on 2.5 cm diameter core and the other on 1.25 cm diameter core. If each spring has V coils, then the ratio of their spring constants would be:

    A) 1/16                             

    B) 1/8

    C) 1/4                               

    D) ½

    Correct Answer: B

    Solution :

    \[{{G}_{1}}={{G}_{2}},\] \[{{d}_{1}}={{d}_{2}},\] \[{{D}_{1}}=2.5\,\,cm,\] \[{{D}_{1}}=1.25\,\,cm,\] \[{{n}_{1}}={{n}_{2}}=n,\] Spring constant, \[k=\frac{G{{d}^{4}}}{8{{D}^{3}}n}\] G, d and n being value \[k\propto \frac{1}{{{D}^{3}}}\] \[\frac{{{k}_{1}}}{{{k}_{2}}}={{\left( \frac{{{D}_{2}}}{{{D}_{1}}} \right)}^{3}}={{\left( \frac{1.25}{2.5} \right)}^{3}}=\frac{1}{8}\]


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