Question Detail
Question
A solid sphere of weight 36 N rolls up an incline at an angle of 30°. At the bottom of the incline the centre of mass of the sphere has a translational speed of 4.90 m/s. Calculate the kinetic energy of the sphere at the bottom of the incline?
Correct Answer
Option C is the correct answer.
Detailed Explanation
Mass m = weight/g = 36/9.8 ≈ 3.673 kg. For a solid sphere, moment of inertia I = (2/5) m R². Total kinetic energy = translational KE + rotational KE = ½ m v² + ½ I ω² = ½ m v² + ½ (2/5 m R²) (v²/R²) = ½ m v² + (1/5) m v² = (7/10) m v². So KE = (7/10) × 3.673 × (4.90)² = 0.7 × 3.673 × 24.01 = 0.7 × 88.18 = 61.73 J ≈ 61.7 J. Option A is 61.7 J.
Hint
For a rolling sphere, total KE = (7/10) m v².