First slide

Applications of SHM

Question

The period of oscillations of mass m = 200 g poured into a bent tube (see figure), whose right arm makes an angle 30^o with the vertical and whose left arm is vertical, is T seconds. The cross-sectional area of the tube is A = 0.5 cm². The value of 10T is ___________. Neglect viscosity.

Moderate

Solution

$\begin{array}{l} T = \sqrt{\frac{m}{A ρ g (\sin θ_{1} + \sin θ_{2})}} \\ = \sqrt{\frac{0.2}{0.5 \times 10^{- 4} 9.8 (\sin 90^{\circ} + \sin 60^{\circ}) \times 13.6 \times 10^{3}}} \\ T = \sqrt{0.5 \times 9.8 (1 + \frac{\sqrt{3}}{2}) \times 13.6 \times 10^{- 1}} = 0.8 s \\ ∴ 10 T = 8 \end{array}$

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