A solid sphere of radius R is placed on an incline that makes an angle θ with the horizontal.The sphere rolls down the incline without slipping.What is its acceleration?

Question

A solid sphere of radius R is placed on an incline that makes an angle ​θ with the horizontal.The sphere rolls down the incline without slipping.What is its acceleration?

Quizplus · Accepted Answer

The acceleration of the sphere can be found using the formula:
a = g*sinθ/(1+(I/m*R^2))
where I is the moment of inertia of the solid sphere and m is its mass.
For a solid sphere, I = (2/5)*m*R^2
Substituting the values and simplifying, we get:
a = (2/7)*g*sinθ
Therefore, the acceleration of the sphere is proportional to sinθ and does not depend on the radius of the sphere.
Option B is the only one that matches this value.

A Solid Sphere of Radius R Is Placed on an Incline