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Questions  

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

a
4 U
b
8 U
c
16 U
d
U4

detailed solution

Correct option is C

Let extension produced in a spring be x initially. In stretched condition spring will have potential energyU = 12kx2Where k is spring constant or force constant∴  U1U2  = x21x22-----------------(i)Given, U1 = U, x1 = 2 cm, x2 = 8 cmPutting these values in Eq.(i), we haveUU2 = (2)2(8)2 = 464 = 116∴  U2 = 16 U

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