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How heavy is 974 grains?

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It's about as heavy as a Battery (C).
In other words, the weight of a Battery (C) is 1 times 974 grains.
(Alkaline)
A "C" size battery weighs 1,000 grains. C batteries are typically used in medium-drain devices such as musical instruments.
It's about one-and-one-tenth times as heavy as a Tennis Ball.
In other words, 974 grains is 1.09 times the weight of a Tennis Ball, and the weight of a Tennis Ball is 0.9170 times that amount.
(ITF Standard; for Type 2 ball)
Per International Tennis Federation standard, regulation tennis balls must weigh about 890 grains. Competition balls are also tested for bounce height, with the standards requiring that a ball dropped from 254 cm must bounce back to a height of 135 cm to 147 cm.
It's about one-and-two-fifths times as heavy as a Golf Ball.
In other words, 974 grains is 1.3740 times the weight of a Golf Ball, and the weight of a Golf Ball is 0.72780 times that amount.
(per R&A USGA Rules of Golf; maximum rule weight)
According to the Rules of Golf (as approved by the United States Golf Association and the Rules Committee of the Royal and Ancient Golf Club of Saint Andrews), golf balls must weigh no more than 708.80 grains. Golf balls are not required to have the familiar dimpled pattern, but the design has been popular since its invention in 1905 because it reduces drag while increasing lift.
It's about two-thirds as heavy as a Deck of Cards.
In other words, the weight of a Deck of Cards is 1.50 times 974 grains.
(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 1,500 grains. 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 3,500,000 grains.
It's about one-and-nine-tenths times as heavy as a Light Bulb.
In other words, the weight of a Light Bulb is 0.530 times 974 grains.
(a.k.a. lamp) (for A19-size, 60w, incandescent bulb by Bulbrite; package weight)
A standard, sixty-watt light bulb weighs about 530 grains. The tightly-coiled filament inside a bulb of this size would measure about 579mm if uncoiled and stretched out.
It's about half as heavy as a Battery (D).
In other words, 974 grains is 0.4680 times the weight of a Battery (D), and the weight of a Battery (D) is 2.140 times that amount.
(Alkaline)
A "D" size battery weighs 2,080 grains. The D size battery is the oldest of the modern battery sizes, first invented by the National Carbon Company in 1898.
It's about two-fifths as heavy as a Baseball.
In other words, 974 grains is 0.434397212543550 times the weight of a Baseball, and the weight of a Baseball is 2.30204055441480 times that amount.
(MLB rules)
Per Major League Baseball rules, a baseball must weigh between 2,187.50 grains and 2,296.8750 grains. 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).