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How heavy is 34.7 fluid drams (ʒ)?

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It's about as heavy as a Battery (D).
In other words, the weight of a Battery (D) is 1 times 34.7 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 nine-tenths as heavy as a Baseball.
In other words, 34.7 fluid drams (ʒ) is 0.9285574912892 times the weight of a Baseball, and the weight of a Baseball is 1.0769392411143 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 four-fifths as heavy as a Billiard Ball.
In other words, 34.7 fluid drams (ʒ) is 0.82762732919255 times the weight of a Billiard Ball, and the weight of a Billiard Ball is 1.2082732949087 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 four-fifths as heavy as a Puck (Hockey).
In other words, 34.7 fluid drams (ʒ) is 0.82762732919255 times the weight of a Puck (Hockey), and the weight of a Puck (Hockey) is 1.2082732949087 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-two-fifths times as heavy as a Deck of Cards.
In other words, the weight of a Deck of Cards is 0.71 times 34.7 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 seven-tenths as heavy as a Hamster.
In other words, the weight of a Hamster is 1 times 34.7 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 two times as heavy as a Battery (C).
In other words, 34.7 fluid drams (ʒ) is 2.1 times the weight of a Battery (C), and the weight of a Battery (C) is 0.48 times that amount.
(Alkaline)
A "C" size battery weighs 17 fluid drams (ʒ). C batteries are typically used in medium-drain devices such as musical instruments.