Two massless springs with spring constants 2 k and 9 k , carry 50 g and 100 g 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

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Two massless springs with spring constants 2 k and 9 k , carry 50 g and 100 g 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 be :

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Correct answer: A. 3 : 2

Maximum velocity is given by v max = &#969; A = k m A Here, k 1 m 1 A 1 = k 2 m 2 A 2 &#8658; 2 k 50 &#215; 10 - 3 A 1 = 9 k 100 &#215; 10 - 3 A 2 &#8658; 2 A 1 = 3 A 2 Thus, ratio of amplitude is A 1 A 2 = 3 2 = 3 : 2 .

Two massless springs with spring constants 2 k and 9 k , carry 50 g and 100 g 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 be :

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