Two massless springs with spring constants 2k and 9k, carry 50g and 100g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then the ratio of their respective amplitudes will

Correct Option - 2


Detailed Solution:

${\omega }_1=\sqrt[]{\frac{k}{m}}=\sqrt[]{\frac{2k}{0.05}}$

$\begin{array}{l}\Rightarrow A_1{\omega }_1=A_2{\omega }_2\\ \frac{A_1}{A_2}=\frac{{\omega }_2}{{\omega }_1}=\sqrt[]{\frac{9k}{0.1}}\times \sqrt[]{\frac{0.05}{2k}}\end{array}$

$\frac{A_1}{A_2}=\frac{3}{2}$

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