Topic pure rolling on inclined plane
For the condition for no slipping why should the force of friction be less than the limiting friction??
When you tend to push a block on a plane ground which can exert friction, if the block is still not moving it means that your force is being cancelled by the frictional force. If you push harder i.e. increase your force, and if the block still doesn't move ... what does it mean?
It means that as you increase your force, frictional force also increases. But upto what level this frictional force can increase? There should be a limit right?
That limit is known as Limiting friction. So if your force is less than or equal to limiting friction, the frictional force can cancel out your force, because it can increase upto this limit. if force is greater than this limiting force, friction will not be able to stop since its limit is reached.
Hence, the answer to your question is if the body is not slipping, it means friction is less than or equal to limiting friction, its not that it should be always less, i.e. it can also be equal.