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Hooke's law is valid for only little deformation. Hooke's principle describes that the extension produced in the wire is directly proportional to the load applied within elastic limit. i.e. within extension, elastic limits load applied.
Later on it was attained that this principle is applicable to all types of deformation such as compression, bending, twisting etc and therefore a modified form of Hooke's law was given as stated below.
"Within elastic limit, the stress developed is directly proportional to the strain produced in a body"
What is the relationship among the period and the square root of the length? The graph is linear, so the period is proportional to the square root of the length of the string.
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