Friction in case of pure rolling I know that friction in pure rolling is zero.But in some questions friction is included such as on an inclined plane while in others friction is not included . I am very much confused with friction in pure rolling. Can anybody clarify me what actually happens and where I am going wrong?
Should we include friction or not and if yes then in which cases?
I have one more doubt that what if any external force is present in case of rolling down for rough and smooth inclined plane? I believe that in smooth incline plane the force will provide the torque and the object will roll down but what in case of rough inclined plane. Also can it perform pure rolling motion without slipping?
 A: Frictional force is not zero in a rolling motion
An object is able to roll only because friction prevents the bottom part from slipping. Else the body would simply slip through the floor. It is true for all kinds of surface-flat, inclined, cicular... 
Work Done by frictional force, during a pure rolling motion is zero

Referring to the animation, we see that the bottom most point, which is in contact with the ground lifts up perpendicular to the direction of force of friction. Thus, No work is done by friction and no energy losses occur during rolling.
When to consider rolling friction and when to not
If you are dealing with problems involving conservation of enrgy, work energy theorem, etc you should not consider work done by friction (since no work. is done) but you should not forget that force of friction do exist. When you are to find the acceleration of a body, or forces on a rolling body, you have to consider the frictional force. 
A problem can be solved in both ways-using work energy theorem or using forces. In general, If your approach is using energy conservation, No frictional losses. If your approach is using force-acceleration, consider the frictional force. I am attaching a problem solved in both ways for a clearer understanding.


A: I think your confusion is due to the fact that there are two types of friction.


*

*One is always zero. That is kinetic friction (it only appears when something slides, which isn't the case for rolling).

*The other is not always zero. That is static friction (it appears to prevent sliding, so it holds on to the contact point whenever there is a tendency to slide).


When you accelerate or brake with your car, the wheels rolling over the surface feel a static friction force. If not, then the wheels would slide over the surface, because they are being slowed down by the engine (via the axle) but nothing is slowing down the car as a whole and so, the wheels will slide over the asphalt.
Also, as in your example, if you roll anything uphill or downhill, gravity pulls downwards and tries to make the contact point slide. Static friction then appears to prevent that sliding. It must thus pull up along the incline (regardless of rolling direction).

I have one more doubt that what if any external force is present in case of rolling down for rough and smooth inclined plane? I believe that in smooth incline plane the force will provide the torque and the object will roll down but what in case of rough inclined plane. 

An external force could for instance be gravity, I guess, unless you are thinking of something specific. But gravity sums up to be pulling in the centre of the wheel. It causes no rotational torque about the centre. So, gravity can't be the thing that causes the rotation. 
Rather, static friction at the contact point makes the wheel rotate.


*

*Is the incline completely smooth, then no static friction is possible. Then no rotation happens and the wheel will simply slide down the incline without ever beginning to spin around. 

*Is the incline rough, then a static friction force is possible, and now this static friction causes a torque that makes the wheel rotate.


In other words, a rough surface is a requirement for pure rolling (or rolling without slipping/sliding) to be possible in such scenario.
A: Sometimes, one point of confusion is due to the difference between friction as a Force and friction as a source for energy losses. In rolling without slipping, friction can exist, but it does not do any work. Therefore, it would not do any work, and it would not cause any energy to be lost. 
However, friction is required to induce any changes in the angular velocity of the object. If an object is rolling along on a plane, there does not need to be any frictional force. However, if there was no friction (or any other forces), there can not be a torque, and there cannot be a change in angular velocity. If we let a cylinder roll without slipping down an incline plane, its angular velocity must be increasing, as its linear velocity is increasing. Therefore, there must be some torque that causes this. Typically in problems this is due to friction. 
This friction is also referred to as traction in rolling type motion. Traction is required to move forward in a car (if you accelerate in a car on frictionless ice, you would skid, and not move forward), but as long as you are not slipping, it does not induce any energy losses, since the point of contact does not slide. 
A: Friction works to ensure pure rolling motion. When an object is not undergoing pure rolling friction, it will adjust its direction to ensure pure rolling and once it has been achieved it will no more be present so it's sole purpose is to make object roll without slipping. In the case of inclined plane friction, it is necessary because no other force is present about center of mass whose torque can make the object roll purely.
