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NEET PHYSICSOscillationsMedium

Question

A second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket:

A

Comes down with uniform acceleration

B

Moves around the earth in a geostationary orbit

C

Moves up with a uniform velocity

D

Moves up with the uniform acceleration

Step-by-Step Solution

  1. Formula: The time period TT of a simple pendulum is given by T=2πLgeffT = 2\pi \sqrt{\frac{L}{g_{eff}}}, where LL is the length and geffg_{eff} is the effective acceleration due to gravity .
  2. Analysis: To decrease the period TT, the effective gravity geffg_{eff} must increase (since T∝1geffT \propto \frac{1}{\sqrt{g_{eff}}}).
  3. Case 1 (Moving up with acceleration aa): When the rocket accelerates upwards, the pseudo-force acts downwards, adding to gravity. Thus, geff=g+ag_{eff} = g + a. Since geff>gg_{eff} > g, the period TT decreases.
  4. Case 2 (Moving down with acceleration aa): Pseudo-force acts upwards. geff=g−ag_{eff} = g - a. TT increases.
  5. Case 3 (Uniform velocity): Acceleration a=0a = 0. geff=gg_{eff} = g. Period remains unchanged.
  6. Case 4 (Geostationary orbit): Inside a satellite orbiting the earth, the effective gravity is zero (geff≈0g_{eff} \approx 0). The pendulum would not oscillate (T→∞T \to \infty).

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Oscillations. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSOscillationssecondspendulummountedrocketperiod

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