Question

Which of the following are in static equilibrium? a) a pendulum at the top of its swing b) a merry-go-round spinning at constant angular velocity c) a projectile at the top of its trajectory (with zero velocity) d) all of the above e) none of the above

Short answer

a) A pendulum at the top of its swing b) A merry-go-round spinning at constant angular velocity c) A projectile at the top of its trajectory (with zero velocity) d) All of the above e) None of the above Answer: e) None of the above

Step-by-step solution

Scenario A: A pendulum at the top of its swing

In this scenario, the pendulum is at the top of its swing, which means that it is momentarily at rest. However, gravity is still acting on the pendulum, causing a downward force. Since there is a net force acting on the pendulum (gravity), it is not in static equilibrium.

Scenario B: A merry-go-round spinning at constant angular velocity

In this case, the merry-go-round is spinning at a constant angular velocity, which means there is no net torque acting on it (since it's not accelerating). However, it is not in translational equilibrium since it is constantly moving (rotating). Therefore, this scenario is not in static equilibrium.

Scenario C: A projectile at the top of its trajectory (with zero velocity)

At the top of its trajectory, a projectile has zero velocity, which means it is momentarily at rest. However, just like in scenario A, gravity is still acting on the projectile, causing a downward force. This results in a net force acting on the object, and hence, this scenario is also not in static equilibrium.

Conclusion

After analyzing all the given scenarios, it's clear that none of them are in static equilibrium. Consequently, the correct answer is option e) none of the above.