Question bank/JEE Main/Physics

A simple pendulum of length 50cm and bob's mass 100g is
oscillating in the air. A damping force f = 0.0693V acts due to air,
where V is speed of bob. At any time it has a amplitude A. How much time
it will take so that amplitude becomes half of initial value.

A1 secB3 secC2 secDnone of these

Show answer and solution▾

$A = A_{0^{e}}\frac{- bt}{2m}$
$\frac{\text{A}_{0}}{2} = \text{A}_{0^{\text{e}}}\frac{- \text{bt}}{2\text{m}} \Rightarrow \frac{\text{bt}}{2\text{m}} = \ln 2$

Source: Grass-G / P-09 Physics paper 26 October.docx