Yes, of course cats and cobras are related. The question is how closely. I reckon you are asking whether they are more closely related to each other than either of them is to animals that don't have that organ, such as humans. The answer is that the Jacobson's organ is a retained ancestral character, not a recently evolved organ. It is present, for example, in lizards and turtles also. Therefore, the common ancestor of all reptiles, birds, and mammals probably had this organ, but it has since been lost in some of the descendants of this common ancestor. That means cats and cobras are only distantly related. Cats are more closely related to humans, than they are to snakes, and snakes are more closely related to birds (which have no Jacobson's organ) than they are to cats. Birds and humans are not closely related even though both lack the Jacobson's organ. It just so happens that both birds and the higher primates (monkeys, apes and humans) have evolved to rely more on their sense of sight than their sense of smell.
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The vomeronasal organ (VNO), or Jacobson's organ, is an auxiliary olfactory sense organ that is found in many animals
The functional vomeronasal system is found in many animals, including all snakes, and lizards, plus many mammals, such as mice, rats, elephants, cattle, dogs, cats, goats, and pigs.
Salamanders perform a nose tapping behavior to supposedly activate their VNO.
Snakes use this organ to sense prey, sticking their tongue out to gather scents and touching it to the opening of the organ when the tongue is retracted.
The organ is well developed in strepsirrhine primates such as lemurs and lorises, developed to varying degrees in New World monkeys, and underdeveloped in Old World Monkeys and apes.
Elephants transfer chemosensory stimuli to the vomeronasal opening in the roof of their mouths using the prehensile structure, sometimes called a "finger", at the tips of their trunks.
Painted Turtles use this organ to use their sense of smell underwater.
In some other mammals, the entire organ contracts or pumps in order to draw in the scents.
Some mammals, particularly felids and ungulates, use a distinctive facial movement called the flehmen response to direct inhaled compounds to this organ. The animal will lift its head after finding the odorant, wrinkle its nose while lifting its lips, and cease to breathe momentarily. Flehmen behavior is associated with “anatomical specialization”, and animals that present flehmen behavior have incisive papilla and ducts, which connect the oral cavity to the VNO, that are found behind their teeth. However, horses are the exception, they exhibit Flehmen response but do not have an incisive duct communication between the nasal and the oral cavity.
House cats often may be seen making this grimace when examining a scent that interests them.
The functional vomeronasal system is found in many animals, including all snakes, and lizards, plus many mammals, such as mice, rats, elephants, cattle, dogs, cats, goats, and pigs.
Salamanders perform a nose tapping behavior to supposedly activate their VNO.
Snakes use this organ to sense prey, sticking their tongue out to gather scents and touching it to the opening of the organ when the tongue is retracted.
The organ is well developed in strepsirrhine primates such as lemurs and lorises, developed to varying degrees in New World monkeys, and underdeveloped in Old World Monkeys and apes.
Elephants transfer chemosensory stimuli to the vomeronasal opening in the roof of their mouths using the prehensile structure, sometimes called a "finger", at the tips of their trunks.
Painted Turtles use this organ to use their sense of smell underwater.
In some other mammals, the entire organ contracts or pumps in order to draw in the scents.
Some mammals, particularly felids and ungulates, use a distinctive facial movement called the flehmen response to direct inhaled compounds to this organ. The animal will lift its head after finding the odorant, wrinkle its nose while lifting its lips, and cease to breathe momentarily. Flehmen behavior is associated with “anatomical specialization”, and animals that present flehmen behavior have incisive papilla and ducts, which connect the oral cavity to the VNO, that are found behind their teeth. However, horses are the exception, they exhibit Flehmen response but do not have an incisive duct communication between the nasal and the oral cavity.
House cats often may be seen making this grimace when examining a scent that interests them.