A simple pendulum of length $L$ is set into motion such that the bob moves along a horizontal circular path and the string makes a constant angle with the vertical. If $T$ is the time period and $F$ is tension in the string then:

F \propto L

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F \propto L^{- 1}

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F \propto T^{2}

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F \propto T^{- 2}

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Solution

The correct options are
A $F \propto L$
D $F \propto T^{- 2}$
$T = \frac{2 π}{w} [i . e . w \propto \frac{1}{T}]$
Horizontal FBD : $F c o s θ = m g$
Vertical: $F s i n θ = \frac{m V^{2}}{L s i n θ} = m w^{2} L s i n θ$
$F \propto w^{2}$
$∴ F \propto T^{- 2}$
and $F \propto L$

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A simple pendulum of length L is set into motion such that the bob moves along a horizontal circular path and the string makes a constant angle with the vertical. If T is the time period and F is tension in the string then:

The correct options are A F∝L D F∝T−2T=2πw [i.e. w∝1T]Horizontal FBD : Fcosθ=mgVertical: Fsinθ=mV2L sinθ=m w2 L sinθF ∝ w2∴F ∝ T−2and F∝L

A simple pendulum of length $L$ is set into motion such that the bob moves along a horizontal circular path and the string makes a constant angle with the vertical. If $T$ is the time period and $F$ is tension in the string then:

The correct options are
A $F \propto L$
D $F \propto T^{- 2}$
$T = \frac{2 π}{w} [i . e . w \propto \frac{1}{T}]$
Horizontal FBD : $F c o s θ = m g$
Vertical: $F s i n θ = \frac{m V^{2}}{L s i n θ} = m w^{2} L s i n θ$
$F \propto w^{2}$
$∴ F \propto T^{- 2}$
and $F \propto L$