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Mechanical Properties Of Fluids

Question
CBSEENPH11020790
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The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8cm the potential energy stored in it is

  • 4U

  • 8U

  • 16U

  • U/4

Solution

C.

16U

Let extension produced in a spring be x initially in stretched condition spring will have potential energy
           straight U space equals 1 half kx squared
where k is spring constant or force constant.
             therefore space space space space space space straight U subscript 1 over straight U subscript 2 space equals space fraction numerator straight x subscript 1 superscript 2 over denominator straight x subscript 2 superscript 2 end fraction space space space space space space space space space space... left parenthesis straight i right parenthesis Given comma space straight U subscript 1 space equals space straight U comma space space space space space space straight x subscript 1 space equals space 2 space cm comma space space space space straight x subscript 2 space equals space 8 space cm putting space these space values space in space Eq. space left parenthesis straight i right parenthesis comma space we space have space space space space space space space space space space space space space space space space space space space space space space space space straight U over straight U subscript 2 space equals space fraction numerator left parenthesis 2 right parenthesis squared over denominator left parenthesis 8 right parenthesis squared end fraction space equals space 4 over 64 equals 1 over 16 therefore space space space space space space space straight U subscript 2 space space equals space 16 straight U space space space space space space space

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