JEE Main 2022 · 24 Jun · Shift 2 · Physics Q36

← JEE Main 2022 · 24 Jun · Shift 2

PhysicsSingle correct+4 / -1Question 36 of 90

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 :

1:2

3:2

3:1

2:3

Answer and worked solution

Official answer: B

Maximum speed. $v_{\max}=A\omega$ with $\omega=\sqrt{k/m}$ .

Angular frequencies. $\omega_1=\sqrt{\dfrac{2k}{0.05}}=\sqrt{40k}$ , $\omega_2=\sqrt{\dfrac{9k}{0.1}}=\sqrt{90k}$ .

Equal $v_{\max}$ . $\dfrac{A_1}{A_2}=\dfrac{\omega_2}{\omega_1}=\sqrt{\dfrac{90}{40}}=\dfrac32$ .

(B)

Topics:Spring-mass systems

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JEE Main 2022 · 24 Jun · Shift 2, Physics question 36