In figure (A), mass ' 2m ' is fixed on mass ' m ' which is attached… | JEE Main 2022 (25 Jul, Shift 1)

Q59JEE Main 2022 · 25 JUL · SHIFT 1Medium

Spring Systems

In figure $(A)$ , mass ' $2m$ ' is fixed on mass ' $m$ ' which is attached to two springs of spring constant $k$ . In figure (B), mass ' $m$ ' is attached to two springs of spring constant ' $k$ ' and ' $2k$ . If mass ' $m$ ' in (A) and in (B) are displaced by distance ' $x$ horizontally and then released, then time period $T_1$ and $T_2$ corresponding to $(A)$ and (B) respectively follow the relation.

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Answer: (a)

(A) mass $3m$ , both springs act: $k = 2k$ , so $T_1 = 2\pi\sqrt{\frac{3m}{2k}}$ .
(B) mass $m$ , $k_{eff} = k + 2k = 3k$ , so $T_2 = 2\pi\sqrt{\frac{m}{3k}}$ .
$\frac{T_1}{T_2} = \sqrt{\frac{3m}{2k}\cdot\frac{3k}{m}} = \sqrt{\frac{9}{2}} = \frac{3}{\sqrt{2}}$
So the answer is (a).

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