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A conical pendulum swings in a horizontal circle. If the angle of the string wit

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Question: A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension and the gravitational force acting on the pendulum bob?

Options:

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

Correct Answer: T = mg cos(θ)

Solution: 

The vertical component of tension balances the weight: T cos(θ) = mg.

A conical pendulum swings in a horizontal circle. If the angle of the string wit

Practice Questions

Q1
A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension and the gravitational force acting on the pendulum bob?
  1. T = mg
  2. T = mg cos(θ)
  3. T = mg sin(θ)
  4. T = mg tan(θ)

Questions & Step-by-Step Solutions

A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension and the gravitational force acting on the pendulum bob?
  • Step 1: Understand that a conical pendulum swings in a circle while the string makes an angle θ with the vertical.
  • Step 2: Identify the forces acting on the pendulum bob: the tension (T) in the string and the gravitational force (mg) acting downwards.
  • Step 3: Recognize that the tension can be broken down into two components: a vertical component (T cos(θ)) and a horizontal component (T sin(θ)).
  • Step 4: Focus on the vertical forces. The vertical component of the tension (T cos(θ)) must balance the weight of the bob (mg).
  • Step 5: Write the equation that represents this balance: T cos(θ) = mg.
  • Conical Pendulum Dynamics – The analysis of forces acting on a pendulum that swings in a horizontal circle, focusing on the relationship between tension and gravitational force.
  • Components of Forces – Understanding how to resolve forces into their vertical and horizontal components, particularly in the context of circular motion.
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