A second pendulum is oscillating in an elevator. If the elevator falls freely towards the Earth, then the time period of the pendulum will become
Correct answer: D. ∞
- A. 0 s
- B. 1 s
- C. 2 s
- D. ∞
Explanation
When an elevator falls freely towards the Earth, the effective acceleration due to gravity (g_effective) inside the elevator becomes zero. This is because both the elevator and the pendulum inside it are accelerating downwards at the same rate as the acceleration due to gravity (g). This state is often referred to as weightlessness.The time period (T) of a simple pendulum is given by the formula:T = 2π√(L/g_effective)Where: * T is the time period * L is the length of the pendulum * g_effective is the effective acceleration due to gravityFor a second pendulum on Earth, the time period is normally 2 seconds (T = 2s).However, during free fall, g_effective = 0. Substituting this into the formula:T = 2π√(L/0)Any number divided by zero approaches infinity. Therefore, the time period of the pendulum becomes infinite. This means the pendulum will not oscillate; it will simply remain in whatever position it was in when free fall began, as there is no restoring force due to gravity.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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