A golf ball has a mass of 50 g, and a speed of 30 m/s. If the speed can be measured within accuracy of 1%, then the uncertainty in the position will be
3.5 × 10–33 m
7.5 × 10–33 cm
2 × 10–33 m
1.39 × 1033 km
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4
Answer:
The uncertainty in the speed of the ball is:
Δ
v
=
0.1
%
o
f
v
=
0.1
100
v
=
0.1
100
(
30
k
g
.
m
/
s
)
=
0.03
m
/
s
Now.
If we assume that the uncertainty in the position of the ball be
Δ
x
, then
By using the uncertainty principle,
Δ
x
⋅
Δ
p
=
h
4
π
Here,
h
is the plank's constant i.e.
6.63
×
10
−
34
J
.
s
⇒
Δ
x
⋅
(
m
Δ
v
)
=
h
4
π
(
∵
Δ
p
=
m
Δ
v
)
⇒
Δ
x
=
h
4
π
m
Δ
v
After plugging in the values, we have:
Δ
x
=
6.63
×
10
−
34
J
.
s
4
π
(
0.05
k
g
)
(
0.03
m
/
s
)
Simplifying it further, we will get:
Δ x = 3.5 × 10 − 32 m
The answer is written up to two significant figures.
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