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)

Explanation

Given ` X = 1 cm `
` = 1 xx 10^(-2) m,`
` K = 500 N/m , m 200 g `
Energy stored `= 1/2 Kx^(2) `
` = 1 / 2 xx 500 xx 10^(-4)`
` = 0.25 J`
Increasein mass `= 0.025 / c^(2) = 0.025 / 9 xx 10^(16)`
Fractional Change of mass `= 0.025 / 9 xx 10^(16) xx 1 / 2 xx 10^(-1) `
` = 0.01388 xx 10^(-6) `
` = 1.4 xx 10^(-18) ` .