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Time period of a pendulum whose bob is immersed in a liquid

This type of question, asked 2 times: 2021 Paper 23, 29 Jul 2022. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 23

    9
    A bob of mass ' mm ' suspended by a thread of length ll undergoes simple harmonic oscillations with time period TT. If the bob is immersed in a liquid that has density 14\frac{1}{4} times that of the bob and the length of the thread is increased by 1/3rd 1/3^{\text{rd~}} of the original length, then the time period of the simple harmonic oscillations will be :-

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  2. Question 2

    29 Jul 2022

    117
    The metallic bob of simple pendulum has the relative density 5 . The time period of this pendulum is 10 s10\text{ }s. If the metallic bob is immersed in water, then the new time period becomes 5xs5\sqrt{x}s. The value of xx will be