Measure of two quantities along with the precision of respective
measuring instrument is
A = 2.5 m s–1 ± 0.5 m s–1
B = 0.10 s ± 0.01 s
The value of A B will be
(a) (0.25 ± 0.08) m
(b) (0.25 ± 0.5) m
(c) (0.25 ± 0.05) m
(d) (0.25 ± 0.135) m
please tell me the correct answer and explain how to solve it
To determine the value of A*B, we need to multiply the values A and B, while considering the precision of their respective measuring instruments.
Let's first calculate the minimum and maximum possible values for A and B by subtracting and adding their uncertainties to their central values, respectively.
For A:
Minimum value = 2.5 m/s - 0.5 m/s = 2.0 m/s
Maximum value = 2.5 m/s + 0.5 m/s = 3.0 m/s
For B:
Minimum value = 0.10 s - 0.01 s = 0.09 s
Maximum value = 0.10 s + 0.01 s = 0.11 s
Now, we need to calculate the minimum and maximum possible values for A*B using the extreme values:
Minimum value of A*B = (2.0 m/s) * (0.09 s) = 0.18 m
Maximum value of A*B = (3.0 m/s) * (0.11 s) = 0.33 m
To express the precision of A*B, we take the difference between the maximum and minimum values and divide it by 2:
Precision = (0.33 m - 0.18 m) / 2 = 0.15 m / 2 = 0.075 m ≈ 0.08 m
Now, we have determined the value of A*B and its precision. Comparing this with the given answer options, we can see that the correct answer is (a) (0.25 ± 0.08) m.