Verified Solution • 2025–26 Session moderate

QJEEM22Ph8d29: JEE Main 2022 Physics - Class 11 JEEM22Ph8d29 Solution: A mass , attached to a horizontal spring, executes SHM with an…

A mass 0.9 kg0.9 \mathrm{~kg} , attached to a horizontal spring, executes SHM with an amplitude A1\mathrm{A}_{1} . When this mass passes through its mean position, then a smaller mass of 124 g124 \mathrm{~g} is placed over it and both masses move together with amplitude A2A_{2} . If the ratio A1A2\frac{A_{1}}{A_{2}} is αα−1\frac{\alpha}{\alpha-1} , then the value of α\alpha will be ___________.

Step-by-Step Verified Solution

(0.9)A1K0.9=(0.9+0.124)A2K0.9+0.124(0.9){A_1}\sqrt {{K \over {0.9}}} = (0.9 + 0.124){A_2}\sqrt {{K \over {0.9 + 0.124}}}

A1A2=0.9+0.1240.9{{{A_1}} \over {{A_2}}} = \sqrt {{{0.9 + 0.124} \over {0.9}}}

=1.0240.9= \sqrt {{{1.024} \over {0.9}}}

=αα−1= {\alpha \over {\alpha - 1}}

α=16\alpha = 16

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