A block of mass 2 kg is attached to one end of a massless spring… | JEE Main 2025 (8 Apr, Shift 2)

Q30JEE Main 2025 · 8 APR · SHIFT 2Medium

Spring Systems

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be

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Answer: (a)

Equilibrium is at the natural length, $x = 2$ m from the wall; compressed to 1 m, so amplitude $A = 1$ m.
$\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{200}{2}} = 10\text{ rad/s}$
Displacement from equilibrium is $(2 - x)$ , so $v = \omega\sqrt{A^2 - (2-x)^2} = 10\left[1 - (2-x)^2\right]^{1/2}$ m/s.
So the answer is (a).

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Spring Systems question from JEE Main 2025 (8 Apr, Shift 2)

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