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A conical pendulum swings with a constant speed. If the angle of the string with

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Question: A conical pendulum swings with a constant speed. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?

Options:

  1. mg/cos(θ)
  2. mg/sin(θ)
  3. mg/tan(θ)
  4. mg

Correct Answer: mg/cos(θ)

Solution: 

Tension T = mg/cos(θ) to balance the vertical component of weight.

A conical pendulum swings with a constant speed. If the angle of the string with

Practice Questions

Q1
A conical pendulum swings with a constant speed. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?
  1. mg/cos(θ)
  2. mg/sin(θ)
  3. mg/tan(θ)
  4. mg

Questions & Step-by-Step Solutions

A conical pendulum swings with a constant speed. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?
Correct Answer: Tension T = mg/cos(θ)
  • Step 1: Understand that a conical pendulum swings in a circular motion while the string makes an angle θ with the vertical.
  • Step 2: Identify the forces acting on the pendulum bob: the weight (mg) acting downwards and the tension (T) in the string acting upwards at an angle.
  • Step 3: Break down the tension (T) into two components: a vertical component (T * cos(θ)) and a horizontal component (T * sin(θ)).
  • Step 4: The vertical component of tension (T * cos(θ)) must balance the weight of the bob (mg) to keep it in equilibrium vertically.
  • Step 5: Set up the equation: T * cos(θ) = mg.
  • Step 6: Solve for tension (T) by rearranging the equation: T = mg / cos(θ).
  • Conical Pendulum Dynamics – Understanding the forces acting on a conical pendulum, including tension and gravitational force.
  • Components of Forces – Breaking down the forces into vertical and horizontal components to analyze motion.
  • Trigonometric Relationships – Using trigonometric functions to relate the angle of the pendulum to the forces involved.
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