Auniform solid sphere rolls down an incline. (a) what must be the incline angle (deg) if the linear acceleration of the center of the sphere is to have a magnitude of 0.13g? (b) if a frictionless block were to slide down the incline at that angle, would its acceleration magnitude be more than, less than, or equal to 0.13g?

Part a)

Part b)

acceleration would be

a = g sin10.5 = 0.18 g

so it is more than the above acceleration

Explanation:

As the sphere rolls down on the inclined plane then in that case the force equation on the sphere is given as

torque equation about the center of the sphere is given as

now we have

now we have

Part b)

acceleration of the object sliding on smooth inclined plane is given as

so this acceleration is more than the acceleration of sphere on same inclined plane

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hi there!

out of the two, (b) precision would be more reasonable.   however, both a and b could be pretty reasonable.

-awesomerepublic   : )