Q.19
The mass and linear dimensions of a rectangular block were measured and the result obtained, and their associated uncertainties, are given in the table.
| mass = (25.0 ± 0.1) g length = (5.00 ± 0.01) cm breadth = (2.00 ± 0.01) cm height = (1.00 ± 0.01) cm |
The density of the block was calculated to be 2.50 g cm-3.
What was the uncertainty in the calculated density?
A ±0.01 g cm-3 B ±0.02 g cm-3 C ±0.05 g cm-3 D ±0.13 g cm-3
Answer: C
Density = mass/volume = mass/(length x breadth x height)
∆D/D = ∆M/M + ∆L/L + ∆B/B + ∆H/H
∆D/2.50 = 0.1/25.0 + 0.05/5.00 + 0.01/2.00 + 0.01/1.00 = 0.021
∆D = 0.021 x 2.50 ≈ ±0.05 g cm-3
Q.20
The given table shows the data measured by a student to calculate the Young modulus for a brass which was in the form of a wire.
| length of wire = (1.5 ± 0.01) m diameter of wire = (1.30 ± 0.01) cm mass of load = (6.00 ± 0.01) g extension of wire = (4.0 ± 0.1) mm acceleration of free fall = (9.81 ± 0.01) m s-2 |
Which of the following contributes most to the uncertainty in the calculated values of the Young modulus?
A measurement of length
C measurement of load
Answer: D
The measurement of extension has the highest percentage uncertainty.
Q.21
The velocity v of a liquid in a pipe was to be determined by measuring the force F on a small disc placed in the centre of the pipe with its plane perpendicular to the flow.
The equation relating F to v is
force F = constant x (velocity v)2
where k is a constant. The velocity v had to be calculated with a maximum uncertainty of 1%.
What is the maximum permissible uncertainty in measuring the force F?
A 0.25% B 0.5%
Answer:
Force F = constant x (velocity v)2
→ (∆F/F) x 100% = 2(∆v/v) x 100% = 2(1%) = 2%
Q.22
The external diameter d1 and internal diameter d2 of a metal tube were quoted as (64 ± 2) mm and (47 ± 1) mm respectively.
What is the percentage error in (d1 – d2)?
A 0.3% B 1% C 6% D 18%
Answer: D
Let r = d1 – d2
= (64 ± 2) mm – (47 ± 1) mm
r = (17 ± 3) mm
(∆r/r) x 100% = (3/17) x 100% = 17.6% = 18% (2sf)
Q.23
The period of oscillation T of a simple pendulum is given by the equation.
T = 2π√(l/g)
where l is the length of the pendulum and g is the acceleration of free fall.
When such a pendulum was used to determine g, the fractional error in the measurement of T was ±x and that for l was ±y. What is the fractional error in the calculated value of g?
A x + y B x – y C 2x – y D 2x + y
Answer: D
T = 2π√(l/g) → g = 4π2l/T2
→ ∆g/g = ∆l/l + 2∆T/T = y + 2x
Q.24
The time taken for a body, dropped from the top of a tower, to fall to the ground was as (2.0 ± 0.1) s. The acceleration of free fall was to be taken as 10 m s-2.
What is the appropriate way to quote the calculated height of the tower?
A (20 ± 0.1) m B (20 ± 0.5) m C (20 ± 1) m D (20 ± 2) m
Answer: D
h = ½ gt2 (in the usual notations)
h = ½ (10)(2.0)2 = 20 m
∆h/h = 2∆t/t
i.e. ∆h/20 = 2(0.1/2.0) → ∆h = 2.0 m
so, h = (20 ± 2) m
Q.25
In an experiment to determine the density of a steel ball, the uncertainty in the measurement of its mass was 1% and that its diameter was 3%.
What is the uncertainty in the calculated density of the steel ball?
A 2% B 4% C 8% D 10%
Answer: D
ρ = m/(πd3/6)
→ (∆ρ/ρ) x 100% = (∆m/m) x 100% + 3(∆d/d) x 100% = 1% + 3(3%) = 10%
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