By what fraction does the mass of a spring change when it is compressed by 1 cm? The mass of the spring is 200 g at its natural length and the spring constant is 500 N m−1
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Solution
Given : x=1 cm =0.01 m mo=0.2 kg
Using energy conservation : P.Ei+K.Ei=P.Ef+K.Ef
∴12kx2+0=0+12mov2⟹v=√kmox
∴v=√5000.2×0.01=0.5 m/s
Mass of the boy while running m=mo√1−(v2c2)2
∴ Fractional increase in the mass Δmmo=mo√1−(v/c)2−momo=[1−(v/c)2]−1/2−1