When a ceiling fan is switched on, it makes 10 revolution in the first 3s. Assuming a uniform angular acceleration, how many rotations it will make in the next 3s?A. 10B. 20C. 30D. 40

To solve this problem, we need to determine how many rotations the fan will make in the next 3 seconds, assuming a uniform angular acceleration.

Step 1: Understand the given information
The ceiling fan makes 10 revolutions in the first 3 seconds.
The angular acceleration is uniform, meaning it is constant throughout the motion.
We need to find the number of rotations in the next 3 seconds.
Step 2: Use the equations of motion for angular displacement
For uniformly accelerated motion, the angular displacement (θ) can be described using the equation:

θ = ω₀t + (1/2)αt²

Where:

θ is the angular displacement in radians or revolutions,
ω₀ is the initial angular velocity (rad/s),
α is the angular acceleration (rad/s²),
t is the time in seconds.
Step 3: Solve for the initial angular velocity (ω₀) and angular acceleration (α)
Let the initial angular velocity be ω₀. Since the fan starts from rest, we have ω₀ = 0. Now, we can calculate the angular acceleration.

In the first 3 seconds, the fan makes 10 revolutions, which is the angular displacement (θ₁). We know the time (t₁) is 3 seconds, so:

θ₁ = ω₀t₁ + (1/2)αt₁² 10 = 0 + (1/2)α(3)² 10 = (1/2)α(9) 10 = 4.5α α = 10 / 4.5 α = 2.22 rad/s²

Step 4: Find the number of rotations in the next 3 seconds
Now, we need to calculate how many rotations the fan will make in the next 3 seconds. The total time will be 6 seconds (t₂ = 3 seconds after the initial 3 seconds).

Using the equation for angular displacement again:

θ₂ = ω₀t₂ + (1/2)αt₂² Since the initial angular velocity is 0, ω₀ = 0:

θ₂ = (1/2)(2.22)(3)² θ₂ = (1/2)(2.22)(9) θ₂ = 10.0 revolutions

Step 5: Conclusion
In the next 3 seconds, the fan will make 20 revolutions in total (10 revolutions in the first 3 seconds and 10 more in the next 3 seconds).

Thus, the correct answer is B. 20.