Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given: Distance (D ± ΔD) = (5.2 ± 0.1) m, time (t ± Δt) = (100 ± 1) s.
To find: Speed (v), the maximum relative error `((triangle"v")/"v")`
Step 1- Calculating Speed
Given - D = 5.2 m, t = 100 s
v = `"D"/"t"`
`= (5.2 " m")/(100 " s")`
= 0.052 m s-1
Step 2 - Calculating relative error
Given - ΔD = 0.1 m; Δt = 1 s
`(triangle"v")/"v" = +- ((triangle"D")/"D" + (triangle"t")/"t")`
`(triangle"v")/"v" = +- ((0.1 " m")/(5.2 " m") + (1 " s")/(100 " s"))`
`= +- (1/52 + 1/100)`
`= +- (100 + 52)/5200`
`= +- 152/5200 " i.e." +- 19/650`
= ± 0.0292 m s-1
APPEARS IN
RELATED QUESTIONS
Define Mean absolute error.
Define relative 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"`
In a workshop, a worker measures the length of a steel plate with Vernier calipers having a least count 0.01 cm. Four such measurements of the length yielded the following values: 3.11 cm, 3.13 cm, 3.14 cm, 3.14 cm. Find the mean length, the mean absolute error, and the percentage error in the measured value of the length.
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.
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:
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 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 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 resistance R = `"V"/"I"`, where V = (50 ± 2) V and I = (20 ± 0.2)A. The percentage error in R is 'x' %.
The value of x to the nearest integer is ______.
If E, L, M, and G denote the quantities as energy, angular momentum, mass, and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M−5G−2 are ______.
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?
Which strategy would best reduce an instrumental error caused by a faulty weighing scale?
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 ______.
The reason behind holding thermometer in the mouth instead of the armpit is to reduce ______.
Constant error can be caused due to ______.
