The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscos

Question

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).

TestHub · Accepted Answer

A = A 0 e − b t 2 m b is related to viscosity 8 = 10 e − b a 40 2 m 5 = 10 e − b C o 2 t 2 m ln 5 4 ln 2 = 40 t × 1.3 t = 40 × ( ln 2 ) × 1.3 ln 5 − 2 ln 2 = 40 × 0.693 × 1.3 1.601 − 2 × 0.693 ≃ 161 sec

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