JEE Main 2022 · 27 Jul · Shift 1 · Physics Q57

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PhysicsInteger+4 / -1Question 57 of 90

A mass 0.9 kg, attached to a horizontal spring, executes SHM with an amplitude $A_1$ . When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude $A_2$ . If the ratio $\dfrac{A_1}{A_2}$ is $\dfrac\alpha{\alpha-1}$ , then the value of $\alpha$ will be ______.

Your answer

Answer and worked solution

Official answer: 16

At the mean position momentum is conserved: $0.9v_1=1.024v_2$ .

Amplitude $A=\frac v\omega=v\sqrt{\frac mk}$ , so $\frac{A_1}{A_2}=\sqrt{\frac{1.024}{0.9}}=\frac{16}{15}=\frac\alpha{\alpha-1}$ .

Answer: 16

Topics:Spring-mass systems Conservation of linear momentum

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JEE Main 2022 · 27 Jul · Shift 1, Physics question 57