An elastic spring of force constant k and natural length $3 l_{0}$ is cut into two parts so that their natural lengths are $2 l_{0}$ and $l_{0}$ respectively. One end of these springs are attached to points P and Q, on a fixed vertical wall and other ends are tied with a block of mass m.

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Cutting a spring of constant k and length 3 l 0 ​ : constant is inversely proportional to length. The 2 l 0 ​ part has k 1 ​ = 2 3 k ​ ; the l 0 ​ part has k 2 ​ = 3 k . At equilibrium (both springs horizontal, block at distance x from the wall, no net force): k 1 ​ ( x − 2 l 0 ​ ) + k 2 ​ ( x − l 0 ​ ) = 0 ⇒ 2 3 ​ ( x − 2 l 0 ​ ) + 3 ( x − l 0 ​ ) = 0 ⇒ x = 3 4 l 0 ​ ​ . So statement (A) is correct. (B) is wrong, and the force constants of the shorter and larger parts are 3 k and 3 k /2 , so (C) and (D) are wrong.

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