Physics-
General
Easy

Question

A wire of length Land radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2 a is stretched with a force 2F, the increase in its length will be

  1. l divided by 4    
  2. l    
  3. l divided by 2    
  4. 2 l    

The correct answer is: l


    Young’s modulus Y equals fraction numerator F L over denominator A l end fraction
    equals fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction
    Since for same material Young’s modulus is same, i e comma
    Y subscript 1 end subscript equals Y subscript 2 end subscript
    orfraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction equals fraction numerator open parentheses 2 F close parentheses left parenthesis 2 L right parenthesis over denominator pi open parentheses 2 a close parentheses to the power of 2 end exponent l ʹ end fraction
    orl to the power of ´ end exponent equals l

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