COMEDK · Physics · 6. Work Power Energy

A body of mass 0.5 kg is dropped from a height of 2 m on the top of the spring of length 0.6 m , fixed vertically on the horizontal table. If the spring is depressed by a distance of 10 cm , then what will be the spring constant of the spring? \(g=10 \mathrm{~ms}^{-2}\)

A \(200 \mathrm{Nm}^{-1}\)
B \(150 \mathrm{Nm}^{-1}\)
C \(1500 \mathrm{Nm}^{-1}\)
D \(2000 \mathrm{Nm}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1500 \mathrm{Nm}^{-1}\)

Step-by-step Solution

Detailed explanation

Total height fallen: \(h = (2 - 0.6) + 0.1 = 1.5\) m By energy conservation: \(mgh = \dfrac{1}{2}kx^2\) \(0.5 \times 10 \times 1.5 = \dfrac{1}{2} \times k \times (0.1)^2\) \(7.5 = 0.005k\) \(k = 1500 \ Nm^{-1}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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