Two simple pendulums with amplitudes θ1 and θ2 have length of strings as l1 and l2 respectively.

Question

Two simple pendulums with amplitudes \(\theta _1\) and \(\theta _2\) have length of strings as \(l_1\) and \(l_2\) respectively. Choose the correct options if the maximum angular accelerations are same.

(1) \(\theta _1l_1 = \theta _2l_2\)

(2) \(\theta _1l_2 = \theta _2l_1\)

(3) \(\theta _1l_1^2 = \theta _2l_2^2\)

(4) \(\theta _1l_2^2 = \theta _2l_1^2\)

Answer 1

Correct option is : (2) \(\theta _1l_2 = \theta _2l_1\)

\(\theta = \theta _0 \sin \left( \sqrt{\frac{g}{l}}t+\phi\right)\)

or \(\alpha = -\frac{9}{l}\theta\)

\(\alpha _{max} = \frac{g}{l}\theta _0\)

\((\alpha _{max})_1 = (\alpha _{max})_2\)

\(\frac{\theta _1}{l_1} = \frac{\theta _2}{l_1}\)