In a simple pendulum, the tension of the string is:
Correct answer: C. T = mg cos θ
- A. T = g cos θ
- B. T = mg sin θ
- C. T = mg cos θ
- D. T = mg
Explanation
The correct answer is C: T = mg cos θ. In a simple pendulum, the tension in the string must balance the component of the gravitational force that acts perpendicular to the arc of the pendulum's swing, which is mg cos θ. Option A is incorrect because g cos θ alone does not represent the tension; it lacks the mass component. Option B is incorrect because mg sin θ is the component of the force parallel to the swing's direction, not the tension. Option D is incorrect because mg represents the full weight of the pendulum bob, which does not account for the angle of the swing.
This question appeared on the UHS MDCAT 2010 paper, which you can sit online with every answer explained.
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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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