A sphere can roll purely on a smooth inclined surface. True or False?

A sphere can roll purely on a smooth inclined surface. True or False? Correct Answer False

For pure rolling, V = Rw at every instant of time, ( where V is the speed of the centre of the sphere & w is its angular speed). On an inclined surface a component of gravity is converting its potential energy to kinetic energy & thus ‘V’ is increasing, so ‘w’ should also increase. This requires presence of torque, which in this case is to be provided by friction. Hence, pure rolling on an incline requires the surface to be rough.
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