Nothing great ever came that easy. – **Kresley Cole**

# Lecture 10 Units and Measurement

**Note : In stating numerical answers, take care of significant figures.**

**Exercise 2.1** Fill in the blanks

(a) The volume of a cube of side 1 cm is equal to …..m^{3}

(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to …(mm)^{2}

(c) A vehicle moving with a speed of 18 km h^{–1} covers….m in 1 s

(d) The relative density of lead is 11.3. Its density is ….g cm^{-3} or ….. kg m^{-3}

**Exercise 2.2** Fill in the blanks by suitable conversion of units

(a) 1 kg m^{2} s^{-2} = …. g cm^{2} s^{-2}

(b) 1 m = …. 1y

(c) 3.0 m s^{-2} = …. km h^{-2}

(d) G = 6.67 x 10^{-11} N m^{2} (kg)^{-2} = (cm)^{3} s^{-2} g^{-1}

**Exercise 2.3** A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J = 1 kg m^{2} s^{-2}. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α^{-1}β^{-2}γ^{2} in terms of the new units.

**Exercise 2.4** Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary :

(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.

**Exercise 2.5** A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance ?

**Exercise 2.6** Which of the following is the most precise device for measuring length :

(a) a vernier callipers with 20 divisions on the sliding scale

(b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale

(c) an optical instrument that can measure length to within a wavelength of light ?