A vertical U-tube contains a liquid. The total length of the liquid co

1.	A vertical U-tube contains a liquid. The total length of the liquid column inside the tube is l. When the liquid is in equilibrium, the liquid surface in one of the arms of the U-tube is pushed down slightly and released. The entire liquid column will undergo a periodic motion.(a) The motion is not simple harmonic motion. (b) The motion is simple harmonic motion. (c) If it undergoes simple harmonic motion, the time period will be 2π√(l/g).(d) If it undergoes simple harmonic motion, the time period will be 2π√(l/2g)
Answer» Correct Answer is: (b, d) Let A = area of cross-section of the tube, ρ = density of liquid. If one surface is pushed down by x, the other surface moves up by x. Net unbalanced force on the liquid column = 2xAρg. Mass of the liquid column = lAρ. Let a = acceleration of liquid column. ∴ -2xAρg = (lAρ)a or a = - (2g/l) x Put ω² = 2g/l. ∴ a = - ω²x . This is SHM with T = 2π/ω = 2π √l/2g.

A vertical U-tube contains a liquid. The total length of the liquid column inside the tube is l. When the liquid is in equilibrium, the liquid surface in one of the arms of the U-tube is pushed down slightly and released. The entire liquid column will undergo a periodic motion.(a) The motion is not simple harmonic motion. (b) The motion is simple harmonic motion. (c) If it undergoes simple harmonic motion, the time period will be 2π√(l/g).(d) If it undergoes simple harmonic motion, the time period will be 2π√(l/2g)

Answer»

Correct Answer is: (b, d)

Let A = area of cross-section of the tube, ρ = density of liquid.

If one surface is pushed down by x, the other surface moves up by x.

Net unbalanced force on the liquid column = 2xAρg.

Mass of the liquid column = lAρ.

Let a = acceleration of liquid column.

∴ -2xAρg = (lAρ)a

or a = - (2g/l) x

Put ω² = 2g/l.

∴ a = - ω²x . This is SHM with T = 2π/ω = 2π √l/2g.