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How heavy is 120 monme (匁)?

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It's about as heavy as a Football (Soccer).
(a.k.a. Soccer, a.k.a. Association Football) (FIFA Law 2 specification)
According to FIFA's Law of the Game number 2, a football must weigh between 110 monme (匁) and 120 monme (匁). An artifact on display at the Smith Art Gallery in Museum in Stirling, Scotland is said to be the world's oldest football and is about one-third to one-half the size of a modern football.
It's about one-and-one-tenth times as heavy as a Football (American).
In other words, 120 monme (匁) is 1.094709163953 times the weight of a Football (American), and the weight of a Football (American) is 0.91348463402740 times that amount.
(a.k.a. "pigskin") (NFL standard)
Per National Football League official rules, an American football must weigh between 105.83821966670 monme (匁) and 113.39809250 monme (匁). Because of NFL regulations, ceremonial considerations, and backup requirements, each NFL Superbowl requires the manufacture of 144 balls exclusively for the event.
It's about one-and-three-tenths times as heavy as a Can of Soup.
In other words, the weight of a Can of Soup is 0.770 times 120 monme (匁).
(for Campbell''s Condensed Tomato Soup, 317.9 ml)
A can of Campbell''s Tomato Soup weighs 93 monme (匁). Cans have been used to store soup and other foods since their invention in 1913, but a dedicated can opener was not developed until cans began to use thinner materials — prior to that time, cans were usually opened using various blunt instruments and tools.
It's about seven-tenths as heavy as a Basketball.
In other words, 120 monme (匁) is 0.721512858060 times the weight of a Basketball, and the weight of a Basketball is 1.38597668610 times that amount.
(NBA official ball standards, Size 7)
A regulation NBA basketball, manufactured by Spalding, is known as a Size 7 ball and weighs 166.317202330 monme (匁). These balls have 4,118 pebbles each with a diameter of 2.5 mm
It's about one-and-a-half times as heavy as a Human Heart.
In other words, the weight of a Human Heart is 0.670 times 120 monme (匁).
(human; adult)
The average human heart weighs about 83 monme (匁). Each minute, the heart pumps between 10 and 20 liters (3 to 5 gallons) of blood through its chambers.
It's about two times as heavy as a Hamster.
In other words, the weight of a Hamster is 0.50 times 120 monme (匁).
(for Syrian hamster, a.k.a. golden hamster, a.k.a. Mesocricetus auratus; adult)
An adult Syrian hamster has a typical weight of about 50 monme (匁). Known for transporting food in the pouches of their cheeks so that they can bury it later, some hamsters can store up to 7,000 monme (匁) of food in their borrows.
It's about two-fifths as heavy as a liter of Water.
In other words, 120 monme (匁) is 0.44998740 times the weight of a liter of Water, and the weight of a liter of Water is 2.2222840 times that amount.
(fresh; 4° C / 39.2° F; maximum density)
Contrary to popular belief, 1 liter (0.0.264172052358148 gal) of water at 4° C / 39.2° F (its point of maximum density) weighs 266.67410 monme (匁) rather than 1 kg exactly. The total volume of water on the planet Earth is about 13,590,000,000,000,000,000 (13.59 quntillion) L (3,590,000,000,000,000,000 gallons).