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Oscillations question

2007 · Q144
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Oscillations question

2007 · Q144

NEETPhysicsOscillationsMCQ+4 / −1
A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible.

When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s2).

AIPMT 2007 Physics - Oscillations Question 36 English
  1. A
    10.0 cm
  2. B
    any value less than 12.0 cm
  3. C
    4.0 cm
  4. D
    8.0 cm
View written solutionFree

Correct answer: A

Mass gets detached at the upper extreme position when pan returns to its mean position. At that point, R=mg−mω2a=0R = mg - m{\omega ^2}a = 0R=mg−mω2a=0,
i.e. g=ω2ag = {\omega ^2}ag=ω2a

⇒a=g/ω2=mg/k \Rightarrow a = g/{\omega ^2} = mg/k⇒a=g/ω2=mg/k

⇒a=2×10200 \Rightarrow a = {{2 \times 10} \over {200}}⇒a=2002×10​   [∵As=ω2=km]\left[\because {As = {\omega ^2} = {k \over m}} \right][∵As=ω2=mk​]

⇒\Rightarrow⇒ a = 1/10 m = 10 cm

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