Question

Two massless springs with spring constants 2k and 9k 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 ______.

Options

• 1 : 2

• 3 : 2

• 3 : 1

• 2 : 3

Answer 1

Two massless springs with spring constants 2k and 9k 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 3 : 2.

Explanation:

In SHM, V_max = ωA

ωA = constant

`A_1/A_2 = omega_2/omega_1 = sqrt(k_2/m_2 xx m_1/k_1) = sqrt((9k)/100 xx 50/(2k)) = 3/2`