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 these vibrational energy of both is same which is correct?

Options

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

Answer

B

Explanation

` n = (1)/(2pi) sqrt((g)/(t)) rArr n prop (1)/(sqrt(1)) rArr (n_(1))/(n_(2)) = sqrt((l_(2))/(l_(1))) = sqrt((L_(2))/(2l_(2)))`
`rArr (n_(1))/(n_(2)) = (1)/(sqrt(2)) rArr n_(2)=sqrt(2) n_(1) rArr n_(2) gt n_(1)`
Energy `E = (1)/(2) m omega^(2) a^(2) = 2pi^(2) m omega^(2) a^(2)`
`rArr (a_(1)^(2))/(a_(2)^(2)) = (m_(2)n_(2)^(2))/(m_(1)n_(1)^(2))` (`:' E` is same)
Given `n_(2) gt n_(1)` and `m_(1) = m_(2) rArr a_(1) gt a_(2)`.