Time period of a simple pendulum is T. The time taken to complete 5/8 oscillations starting from mean position is (α)/12T. The value of α is ______.

Correct answer: 7. 5/8th of oscillation =12+18^th of oscillation π+θ=ωt π+(π)/6=(2π)/Tt (7π)/6=(2π)/Tt t=7T/12

Q90 / 90 · JEE Main 2021 (26 Feb Shift 2) · Physics

Time period of a simple pendulum is $T$ . The time taken to complete $\frac{5}{8}$ oscillations starting from mean position is $\frac{α}{12} T$ . The value of $α$ is $______$ .

Correct answer: 7

Solution

$\frac{5}{8}$ th of oscillation $= {(\frac{1}{2} + \frac{1}{8})}^{th}$ of oscillation
$π + θ = ω t$
$π + \frac{π}{6} = (\frac{2 π}{T}) t$
$\frac{7 π}{6} = (\frac{2 π}{T}) t$
$t = \frac{7 T}{12}$

Hence, the correct answer is 7.

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Solution

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Time period of a simple pendulum is $T$ . The time taken to complete $\frac{5}{8}$ oscillations starting from mean position is $\frac{α}{12} T$ . The value of $α$ is $______$ .