If length of oscillating simple pendulum is made 3 1 times at a place keeping amplitude same, then its total energy (E) will be

T = 2 π g ℓ ω 2 π = 2 π g ℓ ω = ℓ g ∴ ω ∝ ℓ 1 ∴ ω 1 ω 2 = ℓ 2 ℓ 1 = ℓ 1 /3 ℓ 1 = 3 ∴ ω 2 = 3 ω 1 Now E ∝ ω 2 ∴ E 1 E 2 = ω 1 2 ω 2 2 = 3 ∴ E 2 = 3 E 1

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PhysicsSHMEnergyEasy2 minPYQ_2020

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

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$T = 2 π \frac{ℓ}{g}$ $\frac{2 π}{ω} = 2 π \frac{ℓ}{g}$ $ω = \frac{g}{ℓ} ∴ ω \propto \frac{1}{ℓ}$ $∴ \frac{ω _{2}}{ω _{1}} = \frac{ℓ _{1}}{ℓ _{2}} = \frac{ℓ _{1}}{ℓ _{1} /3} = 3$ $∴ ω_{2} = 3 ω_{1}$ Now $E \propto ω^{2}$ $∴ \frac{E _{2}}{E _{1}} = \frac{ω _{2}^{2}}{ω _{1}^{2}} = 3$ $∴ E_{2} = 3 E_{1}$

Stream:MHT_CETSubject:PhysicsTopic:SHMSubtopic:Energy

⏱ 2mℹ️ Source: PYQ_2020

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