A simple pendulum is hanging from a peg inser | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the length of the pendulum be $L$. Initially,the bob is at a horizontal position,so the initial angle $	heta_0 = 90^\circ$. The height of the

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Let the length of the pendulum be $L$. Initially,the bob is at a horizontal position,so the initial angle $	heta_0 = 90^\circ$. The height of the bob relative to the lowest point is $h_0 = L(1 - \cos 90^\circ) = L$.After $n$ collisions,the amplitude is $	heta_n$. The height is $h_n = L(1 - \cos 	heta_n)$.The coefficient of restitution $e$ relates the velocities before and after collision. Since the energy loss is related to the height,the ratio of heights after $n$ collisions is given by $\frac{h_n}{h_0} = e^{2n}$.Given $e = \frac{2}{\sqrt{5}}$,we have $e^2 = \frac{4}{5}$.We want the amplitude $	heta_n Thus,$\frac{h_n}{h_0} Substituting the relation: $(e^2)^n For $n=1$: $0.8 > 0.5$.For $n=2$: $0.64 > 0.5$.For $n=3$: $0.512 > 0.5$.For $n=4$: $0.4096 Thus,after $4$ collisions,the amplitude becomes less than $60^\circ$.

Similar Questions

The instantaneous displacement of a simple pendulum oscillator is given by $x = A \cos \left( \omega t + \frac{\pi}{4} \right)$. Its speed will be maximum at time

$A$ simple pendulum of period $T$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate,its period will

The period of a simple pendulum measured inside a stationary lift is found to be $T$. If the lift starts accelerating upwards with an acceleration of $g/3$,then the time period of the pendulum is

What is the length of a simple pendulum,which ticks seconds (in $m$)?

Two masses $M_{A}$ and $M_{B}$ are hung from two strings of length $l_{A}$ and $l_{B}$ respectively. They are executing $SHM$ with frequency relation $f_{A}=2 f_{B}$,then the relation is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module