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 A2. If the ratio (A1/A2) is (α/α-1), then the value of α will be

Question

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 A2. If the ratio (A1/A2) is (α/α-1), then the value of α will be  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(1/2) kA 2=( p 2/2 m ) ⇒(( A 1/ A 2))2=( m 2/ m 1)=(1024/900) ⇒ ( A 1/ A 2)=(32/30)=(16/15)=(16/16-1) ∴ α=16

21​kA2=2mp2​ ⇒(A2​A1​​)2=m1​m2​​=9001024​ ⇒A2​A1​​=3032​=1516​=16−116​ ∴α=16

$\frac{1}{2} k A^{2} = \frac{p ^{2}}{2 m}$
$\Rightarrow (\frac{A _{1}}{A _{2}})^{2} = \frac{m _{2}}{m _{1}} = \frac{1024}{900}$
$\Rightarrow \frac{A _{1}}{A _{2}} = \frac{32}{30} = \frac{16}{15} = \frac{16}{16 - 1}$
$∴ α = 16$