A mass M is suspended from the lower end of a vertical elastic rod of length L, cross-sectional area A and Young's modulus Y. The rod mass is negligible. If the mass is displaced slightly vertically and released, what is the time period of longitudinal oscillation?
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Question

A mass M is suspended from the lower end of a vertical elastic rod of length L, cross-sectional area A and Young's modulus Y. The rod mass is negligible. If the mass is displaced slightly vertically and released, what is the time period of longitudinal oscillation?

Options

G1 Physics · Accepted Answer

For an elastic rod, ΔL = FL/(YA). Therefore, F = (YA/L)ΔL. Thus the rod behaves like a spring of force constant k = YA/L. Hence, T = 2π√(M/k) = 2π√[ML/(YA)]. Correct option: A.