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MHT CET 202622 AprilMorning Shift
Exam
MHT CET
Year
2026
Date
22 April
Shift
Morning Shift
Subject
Physics
Chapter
Oscillations

MHT CET 2026 · 22 April · Morning Shift · Physics · Oscillations

A particle executes a linear S.H.M of amplitude 3 cm. When it is at...

A particle executes a linear S.H.M of amplitude 3 cm. When it is at 1 cm from the mean position, the magnitude of its velocity is half that of its acceleration at the point. The maximum velocity is

Options

  1. A2\sqrt{2} cm/s
  2. B44 cm/s
  3. C828\sqrt{2} cm/s
  4. D12212\sqrt{2} cm/s

Correct answer

D. 12212\sqrt{2} cm/s

Step-by-step solution

Amplitude A=3A = 3 cm.

Magnitude of velocity at distance xx from the mean position is v=ωA2−x2v = \omega \sqrt{A^2 - x^2}.

Magnitude of acceleration at distance xx is a=ω2xa = \omega^2 x.

Given that at x=1x = 1 cm, v=12av = \dfrac{1}{2} a.

ω32−12=12ω2(1)\omega \sqrt{3^2 - 1^2} = \dfrac{1}{2} \omega^2 (1)

ω8=12ω2\omega \sqrt{8} = \dfrac{1}{2} \omega^2

ω=28=42\omega = 2\sqrt{8} = 4\sqrt{2} rad/s.

Maximum velocity is v_\max = A\omega.

v_\max = 3 \times 4\sqrt{2} = 12\sqrt{2} cm/s.

Answer: 12212\sqrt{2} cm/s
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