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  4. When a body of mass M is hung from a spring, the spring extends by 1 cm. If the body of mass 2 M be hung from the same spring, the extension of spring will be

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Q. When a body of mass M is hung from a spring, the spring extends by 1 cm. If the body of mass 2 M be hung from the same spring, the extension of spring will be

VMMC MedicalVMMC Medical 2007

Solution:

Key Idea: Restoring force is proportional to displacement. When body is hung from a spring and left, it executes SHM, hence $ F=kx=Mg $ where k is spring constant and x the extension produced. Given, $ {{M}_{1}}=M,{{M}_{2}}=2M,{{x}_{1}}=1\,cm $ $ \therefore $ $ {{x}_{2}}=\frac{{{M}_{2}}}{{{M}_{1}}}{{x}_{1}}=\frac{2}{1}\times 1=2\,cm $