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IRINA_888 [86]
3 years ago
5

Prove(show) ''T=2π√(l/g)''​

Physics
1 answer:
Nonamiya [84]3 years ago
6 0

Answer:

Time period for Simple pendulum, T=2\pi\sqrt{\frac{l}{g}

Explanation:

The Simple Pendulum

Consider a small bob of mass m is tied to extensible string of length l that is fixed to rigid support. The bob is oscillating in the plane about verticle.

       Let \theta is the angle made by string with vertical  during oscillation.

Vertical component of the force on bob, F=-mg\sin\theta

Negative sign shows that its opposing the motion of bob.

Taking \theta as very small angle then, \sin\theta\sim\theta

F=-mg\theta    

Let x is the displacement made by bob from its mean position ,

then, \theta=\frac{x}{l}

so, F=-mg\frac{x}{l}                ........(1)

Since, pendulum is in hormonic motion,

as we know, F=-kx

where k is the constant and k=m\omega^{2}

F=-m\omega^2x                   .........(2)

From equation (1) and (2)

-m\omega^2x=-mg\frac{x}{l}

\omega=\sqrt{\frac{g}{l}}

Since, \omega=\frac{2\pi}{T}

\frac{2\pi}{T}=\sqrt{\frac{g}{l}

T=2\pi\sqrt{\frac{l}{g}}

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Mass is simply defined as the quantity of matter present in an object. The mass of an object is constant irrespective of the location of the object.

Weight is simply defined as the gravitational pull on an object. The weight of an object varies from place to place due to gravity.

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Mass and weight are related according to the following equation

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<h3>How to determine the weight on the moon</h3>
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W = mg

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Learn more about mass and weight:

brainly.com/question/14684564

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Two blocks are the same size one block has a higher temperature than the other. Which describes the thermal energy of these bloc
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