Statement I: When a gun is fired it recoils, i.e., it pushes back, with much less velocity than the velocity of the bullet. Statement II: Velocity of the recoiling gun is less because the gun is much heavier than the bullet.

Statement I is true because when a gun is fired, the system (gun and bullet) must conserve linear momentum. Initially, the total momentum is zero; thus, the final momentum of the bullet must be balanced by an equal and opposite momentum of the gun, causing it to recoil. Statement II is also true and provides the correct explanation. Momentum is the product of mass and velocity (p = mv). Since the gun and bullet have equal momentum magnitudes, the recoil velocity of the gun (v_g = m_b * v_b / m_g) is inversely proportional to its mass. Because the gun is significantly heavier than the bullet, its recoil velocity is much smaller than the bullet's forward velocity. Therefore, the gun's greater mass is the direct physical reason for its lower recoil velocity.