Two simple pendulum first of bob mass M1 and length L1 second of bob mass M2 and length L2. M1= M2 and L1=2L2.If these vibrational energy of both is same. Then which is correct

n=12πgl⇒n∝1l⇒n1n2=l2l1=L22L2⇒ n1n2=12⇒n2=2n1⇒n2>n1 Energy, E=12mω2a2=2π2mn2a2⇒ a12a22=m2n22m1n12 (∵E is same ) Given n2>n1 and m1=m2⇒a1>a2

Two simple pendulum first of bob mass M1 and length L1 second of bob mass M2 and length L2. M1= M2 and L1=2L2.If these vibrational energy of both is same. Then which is correct

n=12πgl⇒n∝1l⇒n1n2=l2l1=L22L2⇒ n1n2=12⇒n2=2n1⇒n2>n1 Energy, E=12mω2a2=2π2mn2a2⇒ a12a22=m2n22m1n12 (∵E is same ) Given n2>n1 and m1=m2⇒a1>a2

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Two simple pendulum first of bob mass M₁ and length L₁ second of bob mass M₂ and length L₂. M₁= M₂and L₁=2L₂.If these vibrational energy of both is same. Then which is correct

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Amplitude of B greater than A

Amplitude of B smaller than A

Amplitudes will be same

None of these

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} n = \frac{1}{2 π} \sqrt{\frac{g}{l}} \Rightarrow n \propto \frac{1}{\sqrt{l}} \Rightarrow \frac{n_{1}}{n_{2}} = \sqrt{\frac{l_{2}}{l_{1}}} = \sqrt{\frac{L_{2}}{2 L_{2}}} \\ \Rightarrow \frac{n_{1}}{n_{2}} = \frac{1}{\sqrt{2}} \Rightarrow n_{2} = \sqrt{2} n_{1} \Rightarrow n_{2} > n_{1} \\ Energy, E = \frac{1}{2} m ω^{2} a^{2} = 2 π^{2} m n^{2} a^{2} \\ \Rightarrow \frac{a_{1}^{2}}{a_{2}^{2}} = \frac{m_{2} n_{2}^{2}}{m_{1} n_{1}^{2}} (∵ E is same) \end{array}$