A V-shaped tube contains liquid of total length 4 m. The left arm makes 30° with the horizontal and the right arm makes 90° with the horizontal. Take g = 10 m/s² and neglect viscosity. If ω² = N/4 s⁻², find N.
Physics · Simple Harmonic Motion · time period of linear shm
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Question

A V-shaped tube contains liquid of total length 4 m. The left arm makes 30° with the horizontal and the right arm makes 90° with the horizontal. Take g = 10 m/s² and neglect viscosity. If ω² = N/4 s⁻², find N.

Physics · Simple Harmonic Motion · time period of linear shm

G1 Physics · Accepted Answer

For an asymmetric V-tube, ω² = g(sinα+sinβ)/L. Here, α = 30°, β = 90°, L = 4 m. Thus, ω² = 10[(1/2)+1]/4 = 10(3/2)/4 = 15/4 s⁻². Hence, N = 15.