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 A 1 A 2 is α α - 1 , then the value of α will be _____ .

Step-by-step solution

At mean position, the velocity of the particle in S.H.M. is maximum, so kinetic energy is K E = 1 2 k A 2 , where, k is spring constant. We also know that, kinetic energy is related to momentum as K E = p 2 2 m . Now, from both equations, we have 1 2 k A 2 = p 2 2 m (Here, momentum is conserved) ⇒ A 1   A 2 2 = m 2   m 1 = 1024 900 ⇒ A 1   A 2 = 32 30 = 16 15 = 16 16 - 1 ∴ α = 16