First slide

Applications of SHM

Question

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

Moderate

A

$2 x$
B

$x$
C

$\frac{x}{2}$
D

$\frac{x}{4}$

Solution

Spring is cut into two equal halves so spring constant of each part = 2k
These parts are in parallel so $K_{eq} = 2 K + 2 K = 4 K$
Extension force (i.e. W) is same hence by using $F = kx \Rightarrow 4 k \times x^{'} = kx \Rightarrow x^{'} = \frac{x}{4}$ .

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