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How heavy is 38.28125 fluid drams (ʒ)?

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It's about one-and-one-tenth times as heavy as a Baseball.
In other words, 38.28125 fluid drams (ʒ) is 1.0243902439024 times the weight of a Baseball, and the weight of a Baseball is 0.97619047619051 times that amount.
(MLB rules)
Per Major League Baseball rules, a baseball must weigh between 36.458333333333 fluid drams (ʒ) and 38.28125 fluid drams (ʒ). A major league pitcher can throw a baseball at up to 150 kph (91 mph) (with a fastball pitch).
It's about nine-tenths as heavy as a Billiard Ball.
In other words, 38.28125 fluid drams (ʒ) is 0.91304347826087 times the weight of a Billiard Ball, and the weight of a Billiard Ball is 1.0952380952381 times that amount.
(American-style, WPA specifications)
Per the World Pool-Billiard Association, a billiard ball weight must weigh between 40.104166666667 fluid drams (ʒ) and 43.75 fluid drams (ʒ). According to legend, the difficulty in obtaining elephant ivory for the manufacture of billiard balls in the 19th century inspired the search for a replacement material, which led to the development of the first industrial plastic.
It's about nine-tenths as heavy as a Puck (Hockey).
In other words, 38.28125 fluid drams (ʒ) is 0.91304347826087 times the weight of a Puck (Hockey), and the weight of a Puck (Hockey) is 1.0952380952381 times that amount.
(Ice hockey)
A standard ice hockey puck weighs between 40.104166666667 fluid drams (ʒ) and 43.75 fluid drams (ʒ). Hockey pucks can be shot or passed at speeds of up to 160 kph (99 mph) during games.
It's about one-and-one-tenth times as heavy as a Battery (D).
In other words, the weight of a Battery (D) is 0.909 times 38.28125 fluid drams (ʒ).
(Alkaline)
A "D" size battery weighs 34.7 fluid drams (ʒ). The D size battery is the oldest of the modern battery sizes, first invented by the National Carbon Company in 1898.
It's about seven-tenths as heavy as a Hamster.
In other words, the weight of a Hamster is 1 times 38.28125 fluid drams (ʒ).
(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 fluid drams (ʒ). Known for transporting food in the pouches of their cheeks so that they can bury it later, some hamsters can store up to 6,000 fluid drams (ʒ) of food in their borrows.
It's about one-and-three-fifths times as heavy as a Deck of Cards.
In other words, the weight of a Deck of Cards is 0.63 times 38.28125 fluid drams (ʒ).
(ISO 216 B8 size, a.k.a. "poker size" 63 x 88 mm, 52-card deck)
A deck of 52 ISO 216 B8-size playing cards weighs 24 fluid drams (ʒ). Utilizing nearly 3,700 decks, the record-holding largest card tower was built in early 2010, stood over 3.5 m (11 ft), and weighed over 58,000 fluid drams (ʒ).
It's about half as heavy as a Human Heart.
In other words, 38.28125 fluid drams (ʒ) is 0.48 times the weight of a Human Heart, and the weight of a Human Heart is 2.1 times that amount.
(human; adult)
The average human heart weighs about 80 fluid drams (ʒ). Each minute, the heart pumps between 10 and 20 liters (3 to 5 gallons) of blood through its chambers.