Measurements, Error & uncertainties Questions and Answers 2
Q.13
The true value of a quantity x is x0. In an experiment, the quantity is measured many times and the number N of readings giving a value x is plotted against x.
Which of the following graphs best shows measurements that are precise but not accurate?
Answer: B
Precise ≡ small spread in measurements
Accurate ≡ close to true value (x0)
So, graph B best represents precise measurements with poor accuracy.
Q.14
The power loss P in a resistor can be calculated by measuring the potential difference V and the resistance R, and using the equation P = V2/R.
In the experiment, the uncertainty in V and R was estimated to be 3% and 2% respectively.
What is the uncertainty in the calculated value of P?
A 4% B 7%
Answer: C
P = V2/R
Percentage uncertainty in P,
(∆P/P) x 100% ≈ (2∆V/V) x 100% + (∆R/R) x 100%
= 2(3%) + 2% = 8%
Q.15
The acceleration of free fall g was to be determined by measuring the period of oscillation T and the length l of the simple pendulum, and using the formula
g = 4π2l/T2
In the experiment, the uncertainties in measuring l and T were estimated to be 4% and 1% respectively.
What is the uncertainty in g?
A 2% B 3%
Answer: D
g = 4π2l/T2
→ ∆g/g = ∆l/l + 2∆T/T = 0.04 + 2(0.01) = 0.06 or 6%
Q.16
The volume of a cube was determined by measuring its dimensions with vernier callipers, which can be read with an uncertainty of ±0.1 mm. The length of each side was measured as 30 mm.
What is the approximate uncertainty in the value of its volume?
A 1/27% B 3/10%
Answer: D
V = l3 (in the usual notations)
→ (∆V/V) x 100% = 3(∆l/l) x 100% = 3(0.1/30) x 100% = 1%
Q.17
A resistor is marked as having a value of 4.7Ω ± 2%. The power P dissipated in the resistor, when connected in a simple electrical circuit, was to be calculated from the current in the resistor, which measured as (2.50 ± 0.05) mA.
What is the percentage uncertainty in the calculated value of P?
A 2% B 4%
Answer: C
P = I2R
So, ∆P/P ≈ 2∆I/I + ∆R/R = 2(0.05)/(2.50) + 2/100 = 0.06 = 6%
Q.18
The sides of a rectangular wafer of silicon were measured using vernier callipers to the nearest tenth of a millimetre. The lengths measured by a student were 10.4 mm, 6.3 mm and 2.3 mm.
Which of the following gives the volume of the wafer with appropriate precision?
A 1.5070 x 102 mm3
B 1.507 x 102 mm3
C 1.51 x 102 mm3
D 1.5 x 102 mm3
Answer:
In general, the calculated volume should have no more significant figure than any of the measurements used in the calculations.
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