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 absolute error.
Define Mean absolute error.
Define relative error.
Define percentage error.
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?
In Ohm’s experiments, the values of the unknown resistances were found to be 6.12 Ω, 6.09 Ω, 6.22 Ω, 6.15 Ω. Calculate the (mean) absolute error, relative error, and percentage error in these measurements.
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.
Solve the numerical example.
If the formula for a physical quantity is X = `("a"^4"b"^3)/("c"^(1//3)"d"^(1//2))` and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. Calculate percentage error in X.
If Q = `"X"^"n"/"Y"^"m"` and Δx is absolute error in the measurement of X, Δy is absolute error in the measurement of Y, then absolute error ΔQ in Q is ______.
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 ______.
Time for 20 oscillations of a pendulum is measured as t1 = 39.6 s; t2 = 39.9 s; t3 = 39.5 s. What is the precision in the measurements? What is the accuracy of the measurement?
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 ______.
The least count of the main scale of a screw gauge is 1 mm. The minimun number of divisions on its circular scale required to measure 5 µm diameter of a wire is ______.
What are random errors?
If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.
The reason behind holding thermometer in the mouth instead of the armpit is to reduce ______.
