A simple pendulum of length ' ℓ ' has a bob of mass 'm'. It executes S.H.M. of small amplitude 'A'. The maximum tension in the string is ( g = acceleration due to gravity

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A simple pendulum of length ' ℓ ' has a bob of mass 'm'. It executes S.H.M. of small amplitude 'A'. The maximum tension in the string is ( g = acceleration due to gravity)

TestHub · Accepted Answer

(D) y = A sin ω t T = 2 π g ℓ ​ ​ T 2 π ​ = ℓ g ​ ​ = ω ​ ∴ Tension T m a x ​ ​ = m g cos θ + L m v 2 ​ = m g + L m v 2 ​ cos θ = 1 = m g ( 1 + gL v 2 ​ ) ​ Now, y = A sin ω t ∴ ∴ ​ dt dy ​ = A ω cos ω t dt dy ​ ​ m a x ​ = A ω = A ℓ g ​ ​ = V m a x ​ V m a x 2 ​ = A 2 L g ​ T m a x ​ = mg ( 1 + L 2 g A 2 g ​ ) = mg ( 1 + L 2 A 2 ​ ) ​

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