Home
Class 11
PHYSICS
Following observations were taken with a...

Following observations were taken with a vernier callipers while measuring the length of a cylinder :
`3.29 cm,3.28 cm,3.31 cm,3.28 cm,3.27 cm,3.29 cm,3.20 cm`. Then find :
(a) Most accurate length of the cylinder
(b) Absolute error in each observation
(c) Mean absolute error
(d) Relative error
(e) Percentage error
Express the result in terms absolute error and percentage error.

Text Solution

Verified by Experts

(a) Most accurate length of the cylinder will be the mean length `(barl)`
`barl = (3.19+ 3.28+ 3.29+ 3.31+ 3.28+ 3.27+ 3.29+ 3.30)/(8) = 3.288765 cm or barl = 3.29` cm
(b) Absolute error in the first reading = 3.29-3.29 =0.00 cm
Absolute error in the second reading = 3.29 - 3.28 = 0.01 cm
Absolute error in the third reading = 3.29 -3.29 = 0.00 cm
Absolute error in the forth reading = 3.29 -3.31=-0.02 cm
Absolute error in the fifth reading = 3.29 - 3.28 k= 0.01 cm
Absolute error in the sixth reading = 3.29 - 3.27 = 0.02 cm
Absolute error in the seventh reading = 3.29 - 3.209=0.00 cm
Absolute error in the last reading = 3.29 -3.30 = -0.01
(c) Mean absolute error =` bar(Deltal) = (0.00+ 0.01+0.00+0.02+0.01+0.02+0.00+0.01)/(8) = 0.01 cm `
(d) Relative error in length = `(bar(Deltal))/(barl) = (0.01)/(3.29)= 0.0030395= 0.003`
(e) Percentage in length = `(bar(Delta l))/(barl)xx 100 = 0.003 xx 100 = 0.3 %`
So length `l = 3.29 cm pm 0.01 cm " "` (in terms of absolute error)
or `l= 3.29 cm pm 0.30 %` (in terms percentage error)
Promotional Banner

Topper's Solved these Questions

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise BEGINNER S BOX-1|2 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise BEGINNER S BOX-2|4 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Question|1 Videos

  • SEMICONDUCTORS

    ALLEN |Exercise Part-3(Exercise-4)|50 Videos

Similar Questions

Explore conceptually related problems

The external and internal diameters of a hollow cylinder are measured to be (4.23+-0.01) cm and (3.89+-0.01) cm. The thickness of the wall of the cylinder is

If error in measurement of a length of a cube is 3%, what is error in area of its one side ?

If the length of a cylinder is L = (4.00 +-0.01)cm radius r = (0.250 +- 0.001)cm and mass m = (6.25+- 0.01)g . Calculate the percentage error in determination of density.

The internal and external diameters of a hollow cylinder are measured with the help of a Vernier callipers . Their values are 4.23 +- 0.01 cm and 3.87 +- 0.01 cm , respectively . The thickness of the wall of the cylinder is

The curved surface area of the cylinder is 1760 cm^(2) . And its volume is 12320 cm ^(3) Find its height.

Two cubes each of volume 64 cm^3 are joined end to end together. Find the surface area of the resulting cuboid.

While measuring the acceleration due to gravity by a simple pendulum , a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period . His percentage error in the measurement of g by the relation g = 4 pi^(2) ( l // T^(2)) will be

Draw a line segment of length 7.2 cm and divide it in the ratio 5 : 3. Measure the two parts.

The circumference of a circle is 20 cm and there is an error of 0.02 cm in its measurement. The approximate percentage error in area is …………

In the adjacent figure, the height of a solid cylinder is 10 cm and diameters is 7 cm . Two equal conical holes of radius 3 cm and height 4 cm are cut off as shown the figure. Find the volume of the remaining solid.