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Answer :
Final answer:
The kinetic energy of the merry-go-round after 3.93 s is 422 J. The kinetic energy is calculated using the formula KE = 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity. Therefore, the correct option is B) 422 J.
Explanation:
The moment of inertia of a solid cylinder is I = 1/2 * m * r^2, where m is the mass and r is the radius. To find the mass, we use the formula F = ma, where F is the force applied tangentially, m is the mass, and a is the acceleration. The acceleration can be calculated using a = (r * α) / r, where α is the angular acceleration.
Since the merry-go-round starts from rest, the initial angular velocity ω₀ is 0. We can find the final angular velocity ω using the formula ω = ω₀ + α * t, where t is the time.
Finally, we can substitute the values into the formula for kinetic energy to find KE. Therefore, the correct option is B) 422 J.
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