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Mechanical Properties Of Fluids

Question
CBSEENPH11020652

The young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of

  • 1:2

  • 2:1

  • 4:1

  • 1:1

Solution

B.

2:1

Given comma space straight Y subscript steel space equals space 2 straight Y subscript brass space and space straight L subscript straight s space equals space straight L subscript straight b space and space straight A subscript straight s space equals space straight A subscript straight b comma end subscript
such space that space increment straight L subscript straight s space equals space increment straight L subscript straight b
as space we space know space that comma space young apostrophe straight s space modulus comma
straight Y space equals fraction numerator space stress over denominator strain end fraction space equals space fraction numerator begin display style straight F over straight A end style over denominator begin display style fraction numerator increment straight L over denominator straight L end fraction end style end fraction space equals space fraction numerator straight W increment straight L over denominator straight A increment straight L end fraction
So comma space straight W space equals space fraction numerator FA increment straight L over denominator straight L end fraction space proportional to space straight Y
straight i. straight e. comma space straight W subscript straight s over straight W subscript straight b space equals space fraction numerator straight Y subscript straight s over denominator straight Y subscript straight b space end fraction space equals fraction numerator 2 straight Y subscript straight b over denominator straight Y subscript straight b end fraction equals space 2 over 1
Thus comma space weight space added space to space the space steel space and space brass space wires
space must space be space in space the space ratio space of space 2 space colon 1