Advertisements
Advertisements
Question
Measure of two quantities along with the precision of respective measuring instrument is A = 2.5 ms–1 ± 0.5 ms–1 B = 0.10 s ± 0.01 s. The value of A B will be ______.
Options
(0.25 ± 0.08) m
(0.25 ± 0.5) m
(0.25 ± 0.05) m
(0.25 ± 0.135) m
Advertisements
Solution
Measure of two quantities along with the precision of respective measuring instrument is A = 2.5 ms–1 ± 0.5 ms–1 B = 0.10 s ± 0.01 s. The value of A B will be (0.25 ± 0.08) m.
Explanation:
The resultant significant figure in multiplication and addition is equal to the minimal number of significant figures.
A = (2.5 ± 0.5) ms–1
B = (0.10 ± 0.01) s
X = AB = 2.5 × 0.10
= 0.25 m
`(Δx)/x = (ΔA)/A + (ΔB)/B`
`(Δx)/x = 0.5/2.5 + 0.01/0.10`
`(Δx)/x = 0.075/0.25`,
`Δx` = 0.007
≅ 0.08
∴ AB = (2.5 ± 0.08) m
APPEARS IN
RELATED QUESTIONS
Define absolute error.
Define Mean absolute error.
Define percentage error.
If the measured values of the two quantities are A ± ΔA and B ± ΔB, ΔA and ΔB being the mean absolute errors. What is the maximum possible error in A ± B? Show that if Z = `"A"/"B"`
`(Delta "Z")/"Z" = (Delta "A")/"A" + (Delta "B")/"B"`
Answer the following question.
Show that if Z = `"A"/"B"`, `(triangle"Z")/"Z" = (triangle"A")/"A" + (triangle "B")/"B"`
The masses of two bodies are measured to be 15.7 ± 0.2 kg and 27.3 ± 0.3 kg. What is the total mass of the two and the error in it?
The relative density of a metal may be found by hanging a block of the metal from a spring balance and nothing that in air, the balance reads (5 .00 ± 0.05)N while in water, it reads (4.00 ± 0.05)N. The relative density would be quoted as ______.
A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a2 b3 c5/2d–2. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.
In a Screw Gauge, the fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation, the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with the reference line. Calculate the true reading.
The dependence of g on geographical latitude at sea level is given by `g = g_0(1 + betasin^2Phi)` where Φ is the latitude angle and β is a dimensionless constant. If Δg is the error in the measurement of g then the error in measurement of latitude angle is ______.
A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ______ × 10-6 m.
Reading a graduated cylinder at an angle (parallax error) is a specific example of which type of systematic error?
Systematic errors cause all measurements to shift in the same direction. What does this primarily affect?
What are random errors?
Which of the following is an environmental error?
Zero error of an instrument introduces ______.
Instrumental error can be minimised by ______.
Constant error can be caused due to ______.
