A solid cylinder rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is
A)(5/7)g sin $\theta$
B)(1/2)g sin $\theta$
C)(2/3)g sin $\theta$
D)(3/5)g sin $\theta$
E)(4/5)g sin $\theta$

Question

A solid cylinder rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is 
A)(5/7)g sin $\theta$ 
B)(1/2)g sin $\theta$ 
C)(2/3)g sin $\theta$ 
D)(3/5)g sin $\theta$ 
E)(4/5)g sin $\theta$

Quizplus · Accepted Answer

The linear acceleration of the center of mass of a rolling object on an incline is given by
a = (g sin θ) / (1 + (I / MR²))
where θ is the angle of the incline, M is the mass of the object, R is the radius of the object, and I is the moment of inertia of the object about its center of mass.
For a solid cylinder, I = (1/2)MR².
Substituting the given values, we get
11 = (g sin θ) / (1 + (1/2))
Solving for sin θ, we get
sin θ = (2/3) * (11/9.8)
sin θ ≈ 0.633
Therefore, the closest answer choice is C, which gives (2/3)g sin θ.

A Solid Cylinder Rolls Without Slipping Down an Incline as Shown