The angular amplitude of a simple pendulum is | vedclass

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

Question

(D) The maximum tension in the string of a simple pendulum occurs at the lowest point of its oscillation.At the lowest point,the tension $T$ is given

Vedclass · Accepted Answer

$mg (1+	heta_0^2)$

Vedclass · Answer

(D) The maximum tension in the string of a simple pendulum occurs at the lowest point of its oscillation.At the lowest point,the tension $T$ is given by $T = mg + \frac{mv^2}{l}$,where $v$ is the velocity at the lowest point.Using the principle of conservation of energy,the potential energy at the maximum angular displacement $	heta_0$ is converted into kinetic energy at the lowest point:$mgl(1 - \cos 	heta_0) = \frac{1}{2}mv^2$$v^2 = 2gl(1 - \cos 	heta_0)$Substituting $v^2$ into the tension equation:$T_{\max} = mg + \frac{m(2gl(1 - \cos 	heta_0))}{l}$$T_{\max} = mg + 2mg(1 - \cos 	heta_0)$For small angles,we use the approximation $\cos 	heta_0 \approx 1 - \frac{	heta_0^2}{2}$:$T_{\max} = mg + 2mg(1 - (1 - \frac{	heta_0^2}{2}))$$T_{\max} = mg + 2mg(\frac{	heta_0^2}{2})$$T_{\max} = mg(1 + 	heta_0^2)$

The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will be

Similar Questions

The time period of a simple pendulum is $2 \, sec$. If its length is increased $4$ times,then its period becomes ..... $\sec$.

If the length of the oscillating simple pendulum is made $\frac{1}{3}$ times the original, keeping the amplitude the same, then the increase in its total energy at a place will be: (in $\times$)

The bob of a simple pendulum of length $l$ is made of iron. The pendulum is oscillating over a horizontal coil carrying a direct current. If the time period of the pendulum is $T$,then:

$A$ simple pendulum hangs from the ceiling of a car. If the car accelerates with a uniform acceleration,the frequency of the simple pendulum will

$A$ simple pendulum of frequency $f$ has a metal bob. If the bob is charged negatively and is allowed to oscillate above a large positively charged plate,the frequency will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module