The bob of a simple pendulum having length l | vedclass

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

Question

(C) When the bob is displaced by an angle $	heta$,it rises to a vertical height $h$ above its mean position.By the law of conservation of mechanical

Vedclass · Accepted Answer

$\sqrt{2gl(1 - \cos 	heta)}$

Vedclass · Answer

(C) When the bob is displaced by an angle $	heta$,it rises to a vertical height $h$ above its mean position.By the law of conservation of mechanical energy,the potential energy at the extreme position is converted into kinetic energy at the mean (lowest) position.$mgh = \frac{1}{2}mv_{\max}^2$$v_{\max} = \sqrt{2gh}$From the geometry of the pendulum,the vertical distance from the point of suspension to the bob at the extreme position is $l \cos 	heta$.Therefore,the height $h$ is given by:$h = l - l \cos 	heta = l(1 - \cos 	heta)$Substituting the value of $h$ into the velocity equation:$v_{\max} = \sqrt{2gl(1 - \cos 	heta)}$

The bob of a simple pendulum having length $l$ is displaced from the mean position to an angular position $\theta$ with respect to the vertical. If it is released,then the velocity of the bob at the lowest position is:

Similar Questions

Is the oscillation of a simple pendulum at the centre of the earth possible?

$A$ pendulum is oscillating at a frequency of $8 \,Hz$. Suddenly, the string of the pendulum is clamped at its midpoint. What is the new frequency of oscillations (in $\,Hz$)?

Two pendulums having lengths $1.0 \ m$ and $1.21 \ m$ start oscillating simultaneously in the same phase. They will again come in the same phase after how many oscillations of the smaller pendulum?

$A$ man measures the period of a simple pendulum inside a stationary lift and finds it to be $T$ seconds. If the lift accelerates upwards with an acceleration of $\frac{g}{4}$,then the period of the pendulum will be

$A$ piece of wood has length,breadth and height,'$a$','$b$' and '$c$' respectively. Its relative density is '$d$'. It is floating in water such that the side '$a$' is vertical. It is pushed down a little and released. The time period of $S.H.M.$ executed by it is ($g=$ acceleration due to gravity).

Vedclass Test Series

Exam Paper Generator

Online Exam Module