What is the Direction of Frictional Force in Pure Rolling?

[utkarshakash]

Homework Statement

A wheel of radius 20cm is pushed to move it on a rough horizontal surface. It is found to move through a distance of 60cm on the road during the time it completes one revolution about the centre. Assume that the linear and the angular accelerations are uniform. The frictional force acting on the wheel by the surface is
a)along the velocity of the wheel
b)opposite to the velocity of the wheel
c)perpendicular to the velocity of the wheel
d)zero

Homework Equations

The Attempt at a Solution

Let us suppose that the friction is static and thus pure rolling occurs. The friction will act in the forward direction ie along the direction of velocity.
Since pure rolling occurs
$v=\omega r$
The angular displacement is 2∏ rad
The perimeter of the wheel is 2∏*0.2 metres
Since pure rolling occurs the linear distance covered should be equal to (2∏*0.2)metres as only one revolution occurs. But the actual linear distance covered is 0.6 m. This means that our assumption is incorrect and thus kinetic friction acts in the backward direction. So answer should be (b) but it is (a). Where is the fault?

 

[AJ Bentley]

The wheel is being driven (presumably by an axle) but it is 'slipping'. Think about the point where the wheel is in contact with the ground.
Which way is it sliding?

 

[utkarshakash]

The wheel is being driven (presumably by an axle) but it is 'slipping'. Think about the point where the wheel is in contact with the ground.
Which way is it sliding?

It must be sliding backwards.

 

[AJ Bentley]

If it's sliding backwards, which way is the friction?

 

[utkarshakash]

If it's sliding backwards, which way is the friction?

It must be forward which is the correct answer. Thanks!