JEE Main 2022 · 25 Jul · Shift 1 · Physics Q39

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PhysicsSingle correct+4 / -1Question 39 of 90

In figure (A), mass '2 m' 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.

(A) A block m with a mass 2m fixed on top, between two walls, joined to each wall by a spring of constant k. (B) A block m between two walls, joined by springs of constant k and 2k.

\dfrac{T_1}{T_2}=\dfrac3{\sqrt2}

\dfrac{T_1}{T_2}=\sqrt{\dfrac32}

\dfrac{T_1}{T_2}=\sqrt{\dfrac23}

\dfrac{T_1}{T_2}=\dfrac{\sqrt2}3

Answer and worked solution

Official answer: A

Periods. (A): mass $3m$ , springs in parallel $2k$ : $T_1=2\pi\sqrt{\frac{3m}{2k}}$ . (B): $T_2=2\pi\sqrt{\frac m{3k}}$ .

Ratio $\sqrt{\frac92}=\frac3{\sqrt2}$ .

(A)

Topics:Spring-mass systems

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JEE Main 2022 · 25 Jul · Shift 1, Physics question 39