Oscillations

JEE Main level, single correct, medium

33 of 194

Question 33 of 194

A bob of mass mm suspended by a thread of length ℓ\ell undergoes simple harmonic oscillations with time period T.T. If the bob is immersed in a liquid that has density 14\dfrac{1}{4} times that of the bob and the length of the thread is increased by (13)rd{\left(\dfrac{1}{3}\right)}^{rd} of the original length, then the time period of the simple harmonic oscillations will be:

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Answer: (B) 43T\dfrac{4}{3}T

T=2πℓgT=2\pi \sqrt{\dfrac{\ell }{g}}
geff=g−g4=3g4∴T′=2π4ℓ/33g/4=2π16ℓ9g{g}_{eff}=g-\dfrac{g}{4}=\dfrac{3g}{4} ∴T'=2\pi \sqrt{\dfrac{4\ell /3}{3g/4}}=2\pi \sqrt{\dfrac{16\ell }{9g}}
T′=43TT'=\dfrac{4}{3}T

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