Question

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is

• A. 5:7
• B. 2:3
• C. 2:5
• D. 7:5

Hint:

Rotational inertia reduces translational acceleration in rolling motion.

Answer 1

The Correct Option is B

Step 1: For rolling without slipping: a₁ = gθ1+(2)/(5) = (5)/(7)gθ
Step 2: For slipping without rolling: a₂ = gθ
Step 3: Ratio: a₁ : a₂ = (5)/(7) : 1 = 5:7 normalized = 2:3