B) A baseball of mass 0.15 kg thrown at 100 mph has a momentum of 6.7 kg x m/s. if the uncertainty in measuring this momentum is 1.0 x 10-7 of the momentum, calculate the uncertainty in the baseballs position.
Answer B -
Mass of Baseball = 0.15 kg
Speed = 100 mph or 44.704 m/s [1 mph = 0.44704 m/s]
momentum = 6.7 kg.ms-1
uncertainty in measuring momentum = 1.0 * 10-7
uncertainty in position = ?
We know that,
p * x = h/4 ----------------------A
where, p = uncertainty in momentum
x = uncertainty in position
h = plank's constant (6.62607004 × 10-34 m2 kg / s)
= 3.14
Also,
p = uncertainity in measurement * p
p = 1.0 * 10-7 * 6.7 kg.ms-1
p = 6.7 * 10-7 kg.ms-1
Now put all the values in A
p * x = h/4
6.7 * 10-7 kg.ms-1 * x = 6.62607004 × 10-34 m2 kg/s / 4 * 3.14
x = 6.62607004 × 10-34 m2 kg/s / (4 * 3.14 * 6.7 * 10-7 kg.ms-1)
x = 7.87 * 10-29 m [Answer]
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