Two simple pendulum first of bob mass `M_(1)` and length `L_(1)` second of bob mass `M_(2)` and length `L_(2) M_(1) = M_(2)` and `L_(1)` = 2L_(2)`. if the vibrational energy of both is same which is correct?

Options

A. Amplitude of B greater than A
B. Amplitude of B smaller than A
C. Amplitude will be same
D. None of these

Answer

B

Explanation

Frequency, `n = (1)/(2pi) sqrt((g)/(1)) or n prop (1)/(sqrt(1))`
`therefore" "(n_(1))/(n_(2)) = (1)/(sqrt(2))`
`n_(2) = sqrt(2) n_(1) rArr" "n_(2) gt n_(1)`
Energy, `E = (1)/(2) m omega^(2)a^(2) = 2 pi^(2) mn^(2) a^(2)`
and `a^(2) prop (1)/(mn^(2))" "(because "E is same")`
`(a_(1)^(2))/(a_(2)^(2)) = (m_(2)n_(2)^(2))/(m_(1)n_(1)^(2))`
Given `n_(2) gt n_(1) and m_(1) = m_(2) rArr a_(1) gt a_(2)`
So, amplitude of B smaller than A.