Here's a good clear explanation from Jack of Madras College.
Consider the movement of the block relative to the logs:
When the log makes one revolution it travels
metres. As the block is in contact with the logs, it moves metres along the horizontal plane.
Therefore, the block moves
metres relative to the logs.Now consider the movement of the logs relative to the ground:
When the log makes one revolution it rotates
metres. As it is in contact with the ground it moves metres along the horizontal plane.
Therefore, the log moves
metres relative to the ground.This means the log moves
metres relative to the ground but the block moves metres relative to the logs. Therefore, the block moves metres relative to the ground, which is twice as much as the logs. Thus:-