Question

Determine the period of oscillation of mercury of mass m = 200 g poured into a bent tube whose right arm forms an angle θ = 30° with the vertical. The cross-sectional area of the tube S = 0.50 cm² . The viscosity of mercury is to be neglected.

Answer 1

Volume Sx = S'y

(S/cos θ)y

∴  x = y/cosθ

The restoring force which causes the acceleration of the mercury column

= weight of the portion x + component of the weight of position y along the tube.