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Answer 1

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Q.) How does the time period (T) of a simple pendulum depend on its length (l) ? Draw a graph showing the variation of T with I. How will you use this graph to determine the value of g (acceleration due to gravity) ?

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✏ A pendulum is a simple device in which a Bob is suspending freely on the string making sometime period.

First part :-

Consider forces on the bob, resulting in a net force of −mg sinθ toward the equilibrium position is, a restoring force.

Tension in the string exactly cancels the component mg cosθ || to the string. Henc,e the net restoring force back toward the equilibrium position at θ = 0°.

F ≈ −mgθ

The displacement ∝ θ. When θ (radians), the arc length in a circle is its radius

θ = $\dfrac{s}{L}$

Now, restoring force

F ≈ $\dfrac{-mg}{L}$ s

We know F = -kx

k = $\dfrac{mg}{L}$

Now, the period of a pendulum for amplitudes .

T = 2π $\sqrt{ \</strong><strong>d</strong><strong>frac{m}{k} }$

= 2π $\sqrt{ \dfrac{m}{ \fdrac{mg}{L} } }$

Hence,

T = 2π $\sqrt{ \dfrac{L}{g} }$

This, explains the period of a simple pendulum are its length and the acceleration due to gravity.

Second Part :-

✴ The graph showing the variation of T with I .Refers to the attachment

Third Part :-

To determine the value of g

Time period (t) ∝ √Length (l)

Where, Slope = $\dfrac{T1²-T2²}{l1-l2}$

Slope is constant = $\dfrac{4π²}{g}$

g = $\frac{4π²}{Slope\:of\:T²\:vs\:l}$

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