Which of the following are in static equilibrium? A pendulum at the top of its swing. All of these. A projectile that was launched vertically at the top of its trajectory. A merry-go-round spinning at constant angular velocity. None of these.
The correct answer and explanation is:
Correct Answer: A projectile that was launched vertically at the top of its trajectory.
Explanation:
Static equilibrium is a condition in which an object is at rest and remains at rest, meaning both its linear velocity and angular velocity are zero. For an object to be in static equilibrium, two conditions must be met. First, the net force acting on the object must be zero. Second, the net torque acting on the object must also be zero.
Let us consider each option:
- A pendulum at the top of its swing: Although the pendulum momentarily comes to rest at the top of its swing, it is not in static equilibrium. This is because there is a net torque due to gravity acting to restore the pendulum back to its equilibrium position. This means rotational motion is about to occur, so it fails the condition of zero net torque.
- A projectile that was launched vertically at the top of its trajectory: At the highest point, the projectile has zero vertical velocity and is momentarily at rest. Although gravity acts downward, there is no net horizontal or angular force. The object is not moving or rotating, so it meets the criteria for static equilibrium in that instant. This is the correct answer.
- A merry-go-round spinning at constant angular velocity: While the merry-go-round is not accelerating, it is in dynamic equilibrium, not static equilibrium, because it is in motion. Static equilibrium requires the object to be completely at rest.
- All of these: This is incorrect because only the projectile at the top of its trajectory meets the definition of static equilibrium.
- None of these: This is incorrect because one of the listed situations qualifies.
Therefore, the only correct option is the projectile at the top of its vertical path, which momentarily satisfies both conditions for static equilibrium.