Is it true or false,please justify the answer A sphere cannot roll on a frictionless inclined surface.

Asked by MANISHA MOHANTY | 6th Feb, 2014, 11:07: PM

Expert Answer:

The statement "A sphere cannot roll on a frictionless inclined surface" is true.
 
Consider the sphere of radius R moving down an inclined plane as shown below.
 
 
The normal reaction is balanced by the vertical component of weight. The horizontal component balances against the frictional force and also provides the rolling motion to the sphere.
 
The torque on the sphere is
               τ = Iα
 
The weight of the sphere and normal reaction have no effect on the torque as they are radial forces. Hence, frictional force provides the torque to the sphere.
 
          τ = FR
 
Thus, we have

           FR = Iα
 
If friction is absent, then we have
 
              α = 0
 
Hence, the sphere will not roll.

Answered by  | 7th Feb, 2014, 11:11: AM

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