Question Detail
Question
A solid ball starts from rest and rolls without slipping down the ramp toward the left as shown in the sketch. The height h = 2 meters. The ball's mass is m and its radius is R. What is the ball's final mass center velocity?
Correct Answer
Option D is the correct answer.
Detailed Explanation
For a solid sphere rolling without slipping, conservation of energy gives: mgh = ½ mv² + ½ Iω². With I = (2/5)mR² and ω = v/R, we get mgh = ½ mv² + ½ × (2/5)mR² × (v/R)² = ½ mv² + (1/5)mv² = (7/10)mv². So v² = (10/7)gh, thus v = √(10gh/7).
Hint
Use conservation of energy including rotational kinetic energy.