Two bodies A and B whose masses are in the rati0 1:2 are suspended from two separate massless springs of force constants kA and kB respectively. If the two bodies oscillate vertically such that their maximum velocities are in the ratio 1:2, the ratio of the amplitude A to that of B is:
A. \(\sqrt{\frac{k_{\mathrm{B}}}{2 k_{\mathrm{A}}}}\)
B. \(\sqrt{\frac{k_{\mathrm{B}}}{8 k_{\mathrm{A}}}}\)
C. \(\sqrt{\frac{2k_{\mathrm{B}}}{ k_{\mathrm{A}}}}\)
D. \(\sqrt{\frac{8k_{\mathrm{B}}}{ k_{\mathrm{A}}}}\)
Answer:B
Two bodies A and B whose masses are in the rati0 1:2 are suspended from two separate massless springs of force constants kA and kB respectively. If the two bodies oscillate vertically such that their maximum velocities are in the ratio 1:2, the ratio of the amplitude A to that of B is:
A. \(\sqrt{\frac{k_{\mathrm{B}}}{2 k_{\mathrm{A}}}}\) B. \(\sqrt{\frac{k_{\mathrm{B}}}{8 k_{\mathrm{A}}}}\) C. \(\sqrt{\frac{2k_{\mathrm{B}}}{ k_{\mathrm{A}}}}\) D. \(\sqrt{\frac{8k_{\mathrm{B}}}{ k_{\mathrm{A}}}}\)