Advertisements
Advertisements
प्रश्न
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
उत्तर
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
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 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?
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.
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.
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.
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.
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 ______.
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?
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 strategy would best reduce an instrumental error caused by a faulty weighing scale?
Zero error of an instrument introduces ______.
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 ______.
The reason behind holding thermometer in the mouth instead of the armpit is to reduce ______.
Constant error can be caused due to ______.
