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Two balls of different masses have the s...

Two balls of different masses have the same volume. If the air resistance on both the balls are the same, prove that, when dropped from the same height, the heavier ball reaches the ground earlier.

Text Solution

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Let the mass of one of the balls be m, and the air resistance acting upward, be f.
Hence, total downward force on the ball.
F = mg - f.
`therefore` Acceleration `=(F)/(m) = (mg - f)/(m)`
` = g - (f)/(m)` .
Thus, from the equation, the ball with more mass has a smaller value of `(f)/(m)` and therefore a greater acceleration. so, it reaches the ground earlier.
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