Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
l = (4.00 ± 0.001) cm,
In order to have same precision, we use,
(4.000 ± 0.001), r = (0.0250 ± 0.001) cm,
In order to have same precision, we use, (0.025 ± 0.001) m = (6.25 ± 0.01) g
To find: percentage error in density
Formulae:
1. Relative error in volume, `(Delta"V")/"V" = (2Delta"r")/"r" + (Deltal)/l` ....(∵ Volume of cylinder, V = πr2l)
2. Relative error `(Deltarho)/rho = (Delta"m")/"m" + (Delta"V")/"V"` ....[∵ Density (ρ) = `("mass"("m"))/("volume"("v"))`]
3. Percentage error = Relative error × 100 %
Calculation:
From formulae (i) and (ii),
∴ `(Deltarho)/rho = (Delta"m")/"m" + (2Delta"r")/"r" + (Deltal)/l`
`= 0.01/6.25 + (2(0.001))/0.025 + 0.001/4.000`
= 0.0016 + 0.08 + 0.00025
= 0.08185
From formula (iii),
% error in density = `(Deltarho)/rho xx 100`
= 0.08185 × 100
= 8.185%
Percentage error in density is 8.185%.
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 relative error.
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 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 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.
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = `(A^2B^(1/2))/(C^(1/3)D^3)`, will be:
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 ______.
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 ______.
The mean length of an object is 5 cm. Which of the following measurements is most accurate?
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.
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.
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 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.
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 ______.
A thermometer always reads 2°C higher than the actual temperature because its zero mark is incorrect. What type of error is this?
A student reads a measuring cylinder from above the liquid level, causing the reading to be higher than the actual value. What type of error is this?
Which one of the following is an effective way to reduce systematic errors in an experiment?
If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.
Instrumental error can be minimised by ______.
Error due to non-removal of parallax between pointer and its image in case of magnetic compass needle causes ______.
Constant error can be caused due to ______.
