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

Which of the following plots represents schematically the dependence of the time period of a pendulum,if measured and plotted as a function of the amplitude of its oscillations? (Note: amplitude need not be small)

If a simple pendulum is taken to a place where $g$ decreases by $4\%$,then the time period

$A$ simple pendulum is attached to the roof of a lift. If the time period of oscillation when the lift is stationary is $T$,then the frequency of oscillation when the lift falls freely will be

The sum of kinetic energy and potential energy of a simple pendulum bob is $0.02 \text{ J}$. The speed of the simple pendulum bob at the equilibrium position is approximately: (Consider mass of the bob = $20 \text{ g}$) (in $\text{ m/s}$)

$A$ pendulum suspended from the ceiling of a train has a period $T$,when the train is at rest. When the train is accelerating with a uniform acceleration $a$,the period of oscillation will

Vedclass Test Series

Exam Paper Generator

Online Exam Module