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An elastic spring of unstretched length ...

An elastic spring of unstretched length L and force constant k is stretched by a small length x. It is further stretched by another small length y. Work done during the second stretching is

A

`(ky)/(2)(x+2y)`

B

`(k)/(2)(2x+y)`

C

`ky(x+2y)`

D

`(ky)/(2)(2x+y)`

Text Solution

Verified by Experts

The correct Answer is:
D
`w_1 =(1)/(2) kx^2`
`w_2 =(1)/(2)k(x+y)^2`
Work for x to y expansion
`=(1)/(2)k(x+y)^2-(1)/(2)kx^2`
`=(1)/(2)kpx^2+y^2+2xy]-(1)/(2)kx^2`
`=(1)/(2)k[x^2+y^2+2xy-x^2]`
`=(1)/(2) k[y^2+2xy]`
`=(1)/(2)k y [y+2x]` .
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Knowledge Check

  • A spring of force constant k is stretched by a small length x. The work done in stretchign it further by a small length y is

    A
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