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A spring having spring constant k is cut...

A spring having spring constant k is cut into two parts in the ratio 1:2 Find the spring constants of the two parts.

Text Solution

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Let the initial length of a spring be x.
The spring constant of a particular spring is inversely proportional to its length.
`therefore` kx=constant
When the spring is cut into two parts in the ratio 1:2, the length of the two parts are `x/3` and `(2x)/3` respectively.
If the spring constants of the two parts are `k_1` and `k_2`,
`k_1x/3=kx or , k_1=3k`
and `k_2=(2x)/3=kx or, K_2=(3k)/2`
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