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Loops made from the same wire: radius ratio from the ratio of moments of inertia

The same question, asked 5 times: 3 May 2023 S1*, 3 May 2023 S2, 16 May 2023 S1, 21 Apr 2025 S1*, 12 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S1

    47
    Two circular loops P and Q of radii 'r' and 'nr' are made from the same wire. Moment of inertia of Q is four times that of P about respective axes. The value of 'n' is

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  2. Question 2

    3 May 2023 S2

    21
    Two loops 'A' and 'B' of radii 'R1R_1' and 'R2R_2' are made from uniform wire. If moment of inertia of 'A' is 'IAI_A' and that 'B' is 'IBI_B', then R2R1\frac{R_2}{R_1} is [IAIB=27]\left[\frac{I_A}{I_B}=27\right]

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  3. Question 3

    16 May 2023 S1

    22
    Two loops P and Q of radii R1R_1 and R2R_2 are made from uniform metal wire of same material. IPI_P and IQI_Q be the moment of inertia of loop P and Q respectively then ratio R1/R2R_1/R_2 is (Given IP/IQ=27I_P/I_Q = 27)

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  4. Question 4

    21 Apr 2025 S1

    36
    Two circular loops PP and QQ of radii ' rr ' and ' nrnr ' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is 4 times that of loop P about its axis. The value of n is

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  5. Question 5

    12 May 2026 S2

    106
    Two loops AA and BB of radii R1R_1 and R2R_2 are made from uniform wire. If moment of inertia of loops AA and BB is IAI_A and IBI_B respectively then R1R2\dfrac{R_1}{R_2} is (Given: IAIB=27\dfrac{I_A}{I_B} = 27)

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