Advertisements
Advertisements
प्रश्न
You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for `sqrt(AB)` as ______.
पर्याय
1.4 m ± 0.4 m
1.41 m ± 0.15 m
1.4 m ± 0.3 m
1.4 m ± 0.2 m
Advertisements
उत्तर
You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for `sqrt(AB)` as 1.4 m ± 0.2 m.
Explanation:
When we take significant figures of measured quantities, we also include zeros in significant figures. Here quantities A and b are the measuring quantities thus the number of significant figures in 1.0 m and 2.0 m is two.
`sqrt(AB) = sqrt(1.0 xx 2.0)`
= `sqrt(2)`
= 1.414 m
Here the minimal significant figure is two in the significant figures, 1.0 m and 2.0 n. Thus,
`x = sqrt(AB)` = 1.4
`(Δx)/x = 1/2 [(ΔA)/A + (ΔB)/B]`
= `1/2 0.2 [1/1.0 + 1/2.0]`
= `0.1 [(2.0 + 1.0)/(1.0 + 2.0)]`
`(Δx)/1.4 = 0.1 (3.0/2.0)`
= 2.1 m
`Δx` = 0.2 m rounding to one place of decimal.
∴ `sqrt(AB) = (1.4 +- 0.2)` m.
APPEARS IN
संबंधित प्रश्न
The error in the measurement of the sides of a rectangle is 1%. The error in the measurement of its area is ______.
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 distance travelled by an object in time (100 ± 1)s is (5.2 ± 0.1) m. What are the speed and its maximum relative error?
Find the percentage error in kinetic energy of a body having mass 60.0 ± 0.3 g moving with a velocity of 25.0 ± 0.1 cm/s.
Solve the numerical example.
If the length of a cylinder is l = (4.00 ± 0.001) cm, radius r = (0.0250 ± 0.001) cm and mass m = (6.25 ± 0.01) g. Calculate the percentage error in the determination of density.
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 ______.
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 ______.
The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, calculate the minimum inaccuracy in the measurement of distance.
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 thermometer always reads 2°C higher than the actual temperature because its zero mark is incorrect. What type of error is this?
A laboratory balance shows a mass reading even when no object is placed on the pan. What is the main cause of this error?
A weighing scale that always reads a constant +0.2 kg because its zero mark is misaligned is a clear example of a(n):
If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.
Zero error of an instrument introduces ______.
Instrumental error can be minimised by ______.
Constant error can be caused due to ______.
