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Habib Raju
Asked: 2022-11-04T19:59:17+05:30 In:

Two bodies (M) and (N) of equal masses are suspended from two separate massless springs of spring constants (k_1) and (k_2) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of (M) to the of (N) is.
A. `k_1/k_2`
B. `k_2/k_1`
C. `sqrt(k_1/k_2)`
D. `sqrt(k_2/k_1)`

Two bodies (M) and (N) of equal masses are suspended from two separate massless springs of spring constants (k_1) and (k_2) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of (M) to the of (N) is.
A. `k_1/k_2`
B. `k_2/k_1`
C. `sqrt(k_1/k_2)`
D. `sqrt(k_2/k_1)`
Parabola
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  1. Correct Answer – D
    `v_(max)=A_Momega_M=A_Nomega_N`
    `A_M/A_N=omega_N/omega_M=sqrt((k_2lm)/(k_1lm))=sqrt(k_2/k_1)`

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Dhanush Mehrotra
Asked: 2022-11-04T07:31:44+05:30 In:

Two bodies (M) and (N) of equal masses are suspended from two separate massless springs of spring constants (k_1) and (k_2) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of (M) to the of (N) is.
A. (k_1)/k_2)
B. sqrt(k_1)//(k_2)
C. (k_2)/(k_1)
D. sqrt(k_2)//k_1)

Two bodies (M) and (N) of equal masses are suspended from two separate massless springs of spring constants (k_1) and (k_2) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of (M) to the of (N) is.
A. (k_1)/k_2)
B. sqrt(k_1)//(k_2)
C. (k_2)/(k_1)
D. sqrt(k_2)//k_1)
Parabola
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1 Answer

  1. Correct Answer – D
    Both the bodies oscillate in simple harmonic motion, for the maximum velocities will be
    Given that `v_1 = v_2 rArr a_1 omega_1 = a_2 omega_2`
    :. `a_1 xx (2 pi)/(T_1) = a_2 xx (2 pi)/(T_2)`
    `rArr (a_1)/(a_2) = (T_1)/(T_2) = (2 pi sqrt(m)/(k_1))/(2 pi sqrt(m)/(k_2)) = sqrt(k_2/(k_1))`.

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