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JEE Main 202529 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Evening Shift
Subject
Physics
Chapter
Oscillations

JEE Main 2025 · 29 January · Evening Shift · Physics · Oscillations

Two bodies A and B of equal mass are suspended from two massless...

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1k_1 and k2k_2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of AA to the maximum velocity of BB is

Options

  1. Ak1k2\frac{\mathrm{k}_1}{\mathrm{k}_2}
  2. Bk1k2\sqrt{\frac{\mathrm{k}_1}{\mathrm{k}_2}}
  3. Ck2k1\sqrt{\frac{\mathrm{k}_2}{\mathrm{k}_1}}
  4. Dk2k1\frac{\mathrm{k}_2}{\mathrm{k}_1}

Correct answer

B. k1k2\sqrt{\frac{\mathrm{k}_1}{\mathrm{k}_2}}

Step-by-step solution

V1=A1ω1 V2=A2ω2 A1=A2 V1 V2=ω1ω2=K1 m K2 m V1 V2=K1 K2\begin{aligned} & \mathrm{V}_1=\mathrm{A}_1 \omega_1 \\ & \mathrm{~V}_2=\mathrm{A}_2 \omega_2 \\ & \mathrm{~A}_1=\mathrm{A}_2 \\ & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\frac{\omega_1}{\omega_2}=\frac{\sqrt{\frac{\mathrm{K}_1}{\mathrm{~m}}}}{\sqrt{\frac{\mathrm{~K}_2}{\mathrm{~m}}}} \\ & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\sqrt{\frac{\mathrm{K}_1}{\mathrm{~K}_2}}\end{aligned}
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