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Two springs of force constants K and 2K ...

Two springs of force constants K and 2K are stretched by the same force. If `E_(1)` and `E_(2)` are the potential energies stored in them respectively then

A

`E_(1) = E_(2)`

B

`E_(1) = 2E_(2)`

C

`E_(1) = (E_(2))/(2)`

D

`E_(1) = (E_(2))/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
If x is the extension for a spring constant k, then for spring
constant 2k, the extension will be `(x)/(2)`
`E_(1) = (1)/(2) kx^(2) E_(2) = (1)/(2) 2k((x)/(2))^(2) = (1)/(4) kx^(2)`
` :. E_(1) = 2E_(2)`
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