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F = kx
First we'll set a comparable value of the extension.
That is, we'll find extension for ONE Load acting on ONE spring.
Let load be W, extension be e.
W = ke,
k = W/e
k is spring constant.
Now we'll find all extensions for the choices in terms of e.
A: Two springs: One load.
W divided equally so each spring takes W/2.
F = kx,
So: W/2 = W/e * x,
x = W/2 *e/W
x = 0.5 e
B: Same set-up as in A. Except the two-spring has another two-spring attached to it.
We'll double the extension. (In series u double ext.)
x = e
C: One single-spring attached to a double-spring set-up.
Single spring will take the whole of load W.
Initially, if u refer to the starting of this reply, u'll see the extension is: e, for a load of W. (That is when the spring takes the whole of the load!)
So for single-spring: ext. is e.
For double-spring set-up, well - just look at A.
x was 0.5 e...
Total ext. for C is: e + 0.5e = 1.5e
D: Single-spring, again, will have ext. e. (Like I said above.)
Triple spring. Each spring takes W/3 load.
F = kx.
W/3 = W/e * x,
x = W/3 * e/W,
x = e/3.
Total ext. for D: e/3 + e = 4e/3 or 1.33e
Compare 'em all.
C has gr8est ext. C's ur answer.
Hope I was of assistance!
