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Two identical straight wires PQ and RS each of mass m and length $l$ can move smoothly on a fixed rectangular frame. Two thin films of a liquid of surface tension T are formed between each wire and the frame. If the two wires are connected by a massless spring of stiffness constant k, initially in natural length position and released then choose the correct option(s).

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Maximum elongation of spring, $Δ x_{m} = \frac{4 T l}{k}$

Each wire executes SHM with time period, $T_{0} = 2 π \sqrt{\frac{2 m}{k}}$

Maximum elongation of spring, $Δ x_{m} = \frac{2 T l}{k}$

Each wire executes SHM with time period, $T_{0} = 2 π \sqrt{\frac{m}{2 k}}$

answer is B, C.

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Detailed Solution

$2 \times 2 T l x = \frac{1}{2} k {(2 x)}^{2}; x = \frac{2 T l}{k}, Δ x_{m} = \frac{4 T l}{k} F_{n e t} = 2 T l - 2 k x; T_{0} = 2 π \sqrt{\frac{m}{2 k}}$

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