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Two springs A and B are identical but A ...

Two springs A and B are identical but A is harder than `B(k_A gt k_B)` . Let `W_A and W_B` represent the work done when the springs are stretched through the same distance and `W'_A and W'_B` are the work done when these are stretched by equal forces, then which of the following is true

A

`W_A gt W_B and W'_A = W'_B`

B

`W_A gt W_B and W'_A lt W'_B`

C

`W_A gt W_B and W'_A gt W'_B`

D

`W_A lt W_B and W'_A lt W'_B`

Text Solution

Verified by Experts

The correct Answer is:
B
`k_A gt k_B` , x is the same
`1/2 k_A x^2 gt 1/2 k_B x^2 implies W_A gt W_B`
Now forces are the same
`k_Ax_A = k_Bx_B` As `k_A gt k_B implies x_A lt x_B`
`W._A=1/2 (k_Ax_A)^2 and W._B=1/2 (k_B x_B) x_B`
`implies W._A lt W._B`
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