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 the above

Answer

B

Explanation

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