NEET 2025 · PhysicsPrevious Year Question
In an oscillating spring-mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically, so the average angular frequency ω(t) and the average amplitude A(t) of the system change with time t. Which option correctly and schematically depicts these changes?
- A.
- B.
- C.
- D.✓
Correct Answer
(D)
Solution & Explanation
Correct Answer (D): D. Step-by-step solution: 1. Angular frequency ω = √(k/m). As sand leaks out, m decreases, so ω INCREASES with time. 2. With sand lost predominantly at the turning points (extreme positions where KE = 0), the mechanical energy is essentially retained while m falls; analysis of E = ½ m ω² A² with k fixed shows the amplitude A INCREASES as mass decreases. 3. Therefore both ω(t) and A(t) increase with time — the schematic showing both curves rising.
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