Chapter 2 : Units and Measurement

Why is this ratio so large ?

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- MLT
- MLT2
- None of the above
- MLT−2

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- A vernier callipers with 20 divisions on the sliding scale.
- A screw gauge of pitch 1 mm and 100 divisions on the circular scale.
- An optical instrument that can measure length to within a wavelength of light.
- All instruments have same precision.

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(a) y=asin 2πt/T

(b) y = a sin υ t

(c) y = (a/T) sin t/a

(d) y = (a/√2) (sin 2π / T + cos 2π / T)

(a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.

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Fill in the blanks

(a) The volume of a cube of side 1cm is equal to ________ m3(b) The surface area of a solid cylinder of radius 2.0cm and height 10.0cm is equal to ________ (mm)2

(c) A vehicle moving with a speed of 18km/h covers ________ metres in one second.

(d) The relative density of lead is 11.3. Its density is ________ g/cm3 or ________kg/m3

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(a) 1 kgm2/s2=.........gcm2/s2

(b) 1 m = .......... ly

(c) 3.0 m s−2 = .........km h−2

(d) G = 6.67 × 10−11 N m2 (kg)−2 = .......... (cm)3 s−2 g−1

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(a) You are given a thread and a metre scale. How will you estimate the diameter of the thread?

(b) A screw gauge has a pitch of 1.0mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?

(c) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?

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- 4
- 3
- 2
- none of the above

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- 100 unit
- 500 unit
- 20 unit
- 2 unit

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Explain this statement clearly:

"To call a dimensional quantity 'large' or 'small' is meaningless without specifying a standard for comparison." In view of this, which of the following statements are complete :(a) atoms are very small objects

(b) a jet plane moves with great speed

(c) the mass of Jupiter is very large

(d) the air inside this room contains a large number of molecules

(e) a proton is much more massive than an electron

(f) the speed of sound is much smaller than the speed of light.

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P a3b2 / √c d

The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?

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m=mo(1−v2)1/2

Guess where to put the missing c.

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(a)0.007m2

(b)2.64×1024kg

(c)0.2370gcm−3

(d)6.320J

(e)6.032Nm−2

(f)0.0006032m2

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- 4
- 3
- None of the above
- 5

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- 0.035mm
- 0.007mm
- 3.5mm
- None of the above

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