The length of a spring is l and its force constant is k. When a weight W is suspended from it, its length increases by x. If the spring is cut into two equal parts and put in parallel and the same weight W is suspended from them, then the extension will be
$(a) 2x (b) x (c) \frac{x}{2} (d) \frac{x}{4}$
Text Solution
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Spring is cut into two equal halves so spring constant of each part = 2k
These parts are in parallel so $K_{eq} = 2K + 2K = 4K$
Extension force (i.e. W) is same hence by using $\mathbf{F} = k \mathbf{x}$ ⇒ ⇒ $4k \times x' = kx$ ⇒ ⇒ $x' = \frac{x}{4}.$
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