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How heavy is 5.250 ounces?

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It's about one-and-one-tenth times as heavy as a Baseball.
In other words, 5.250 ounces is 1.0243902439024 times the weight of a Baseball, and the weight of a Baseball is 0.976190476190510 times that amount.
(MLB rules)
Per Major League Baseball rules, a baseball must weigh between 5 ounces and 5.250 ounces. A major league pitcher can throw a baseball at up to 150 kph (91 mph) (with a fastball pitch), with record-setting pitches as fast as 171 kph (106 mph).
It's about nine-tenths as heavy as a Billiard Ball.
In other words, 5.250 ounces is 0.913043478260870 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 5.50 ounces and 6 ounces. 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, 5.250 ounces is 0.913043478260870 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 5.50 ounces and 6 ounces. 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 0.9090 times 5.250 ounces.
(Alkaline)
A "D" size battery weighs 4.760 ounces. 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 5.250 ounces.
(for Syrian hamster, a.k.a. golden hamster, a.k.a. Mesocricetus auratus; adult)
An adult Syrian hamster has a typical weight of about 7 ounces. Known for transporting food in the pouches of their cheeks so that they can bury it later, some hamsters can store up to 900 ounces 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 0.630 times 5.250 ounces.
(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 3.30 ounces. 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 8,000 ounces.
It's about half as heavy as a Human Heart.
In other words, 5.250 ounces is 0.480 times the weight of a Human Heart, and the weight of a Human Heart is 2.10 times that amount.
(human; adult)
The average human heart weighs about 11 ounces. Each minute, the heart pumps between 10 and 20 liters (3 to 5 gallons) of blood through its chambers.