TUTORIAL 1 (PHYSICAL QUANTITIES AND MEASUREMENTS) 1. Define : (i) Physical quantity (ii) Base quantity (iii) Derived quantity

2. Express :

(a) 24.5 mm in cm (c) 582.2 mm in m (e) 19.256 kg in g (g) 42.3 cm2 in mm2 (i) 1 tones in kg

(b) 0.694 km in m (d) 6.3 g in kg (f) 1.00 g in kg (h) 2.4 m3 in cm3 (j) 10-6 g/cm3 in kg/m3

[ 2.45cm, 694m, 582.2 x 10-3m, 6.3 x 10-3kg, 19.256 x 103g, 1 x 10-3kg, 42.3 x 102mm2, 2.4 x 106 cm3 , 1000kg, 10-3kg/m3 ]

3. What factor corresponds to the following prefixes : (i) nano (ii) giga (iii) deka (x) mikro (iv) centi (v) mega (vi) kilo (vii) piko (ix) Angstrom

4. Convert the following unit to S.I unit : (1 gal = 3.785 l)(a) 8.50 gal/h (b) 100 (mi/h)/s (c) 0.2 g/cm3 [8.93 x 10-3L/s] [ 44.69 m/s2] [2 x 102kg/m3] [4.25m3] (e) The radius of the earth is 6.4 x 106 m and mass 6.0 x 1024kg. The radius of the sun is 108 m and its mass is 2.0 x 1030 kg. What is the ratio of the suns density to that of the earth? 5. What is meant by dimension and state its three applications. (a) The viscous force, F when a metal sphere is going its way downward is given by the equation : F = A a r b v c A = dimensionless constant = coefficient of viscosity of the fluid (unit : kgm-1s-1) , where : [87.38 ]

(d) A wood is 10 ft long, 5ft high and 3ft wide. Express this volume in cubic meters.

r = radius of the metal sphere v = velocity of the metal sphere Determine the values of a, b and c and write down the formula again. [ a =1, b=1, c =1 ] 6. Prove that the given formula below is consistent in terms of dimension. W = g r2 h , where : W = weight of water inside the capillary tube = density of the water g = gravitational acceleration r = radius of the capillary tube and h = height of the capillary tube

7. Show that the equation is dimensionally correct : v2 = u2 2gs

8. Show that the expression = (0 + at) is dimensionally correct, where and 0 representthe speeds, a is acceleration, and t is a time interval.

9. The displacement of a particle when moving under uniform acceleration is some function ofthe elapsed time and the acceleration. Suppose we write this displacement, s = (k am tn) where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. Can this analysis give the value of k? 10. The period T of a sample pendulum is measured in time units and is given by : T = 2

l g

Where l the length of the pendulum and g is the free fall acceleration in units of length divided by the square of time. Show that this equation is dimensionally correct.

11. Newtons law of universal gravitation is :

F=

GMm r2[ G : kg-1 m3 s-2]

Here F is the force of gravity, M and m are masses and r is length. Force has the SI unit of kg m s-2. What are the SI units of the constant G?

12. The dimensions of quantities P and Q are MLT -2 and L2 respectively. What is the base unitsof the quantity X, which is defined as X = P/Q? [kgm-1s-2]

13. Given the expression speed = k (density), find the dimensions for k.

[M-1L4T-1]

14. A sphere of radius r moves at speed v in a viscous fluid. The sphere is acted on by aviscous force F which is given by F = krv. Determine the dimensions and unit of k. [ML-1T-1 , kgm-1s-1]

15. A student suggested that the force F acting on a vertical wall due to a horizontal jet of liquidstriking the wall is given by the expression : F = kAv k = dimensionless constant = density of the liquid A = cross-sectional area of the jet v = speed of the jet Is the expression dimensionally correct?

16. A wire of mass m and length l is stretched so that the tension in the wire is F. When thewire vibrates in a transverse manner, the speed of the transverse waves traveling along the wire is v. Using the method of dimensional analysis, determine an expression for v in terms [v = k

of F, m and l . 17. (i) What is scalar quantity? (give 3 example of scalar quantity) (ii) What is vector quantity? (give 3 example of vector quantity)

Fl ] m

18. Perform graphically the following vector additions and subtractions, where A, B, and C arethe vectors shown in Fig. 1 below:

A B C Figure 1

a) A + B

b) A + B + C

c) A B

d) A + B C

19. Let A = 20 i 10j + 30 k and B = -6i + 15 j 25k . Find : a. the magnitudes of A and B

[ A = 37.42 , B = 29.77 ]

b. the vector product C = A X B c. the angle between A and B

[C = 200(-i + 1.6j + 1.2k) ] [ = 23.67]

20. Use unit vectors to find the vector sum of a displacement A of 2.0 m at 30 and adisplacement B of 2.5 m at 133 counterclockwise. (All calculation in one decimal point) 21. Express each of the following numbers in scientific notation. (i) 360,000 (ii) 0.000248 (iii) 12.104 (iv) 6.28 (v) 562 [ 3.6 x 105, 2.48 x 10-4, 1.2104 x 101, 6.28 x 100, 5.62 x 102] 22. How many significant figures are there in each of the following numbers : (a) 32.46 (b) 3.002 (c) 0.1040 (d) 0.0024 (e) 2000 [2.8 m] j

23. How many significant figures are in each of these measurements? a) 6.78 g b) 0.304 kg c) 0.058 m d) 7.58 x 105 g g) 2.3 x 104 s e) 5.30 x 103 kg f) 9.7 x 10-2 m

24. In these calculations, be sure to use an appropriate number of significant figures.a) 3.463 x 105 1.68 x 107 b)

6.379 x10 3 6.1023x10 26

25. Perform the following calculations quoting the answers to the correct number of significant figures : (a) 13.28m + 2.06m + 0.48m (c) 2.42 x 0.06 (e) 18.62/2.02 (b) 106g + 32g + 4.9g + 2.68g (c) 8.62/ 1.5 (d) 4.2 x 10-2 x 5.01 x 10-3 (f) (8.6 x 2.48) / 0.12

(g) Area of a rectangle 10.0cm long and 1.50cm wide (h) Area of a circle of radius 4.0cm (i) Density of a gas if 6.0m3 weighs 0.038kg (j) Average speed when a distance of 100m is covered in 10.5s. [ 16m, 1.5 x 102g , 0.1, 2.1 x 10-4, 9.22, 1.8 x 102 , 15.0cm2 , 50cm2 , 6.3 x 10-3kgm-3 , 9.52 m/s ]

26. Consider this set of results from the measurement of the length of a metal rod : (All measurements are in centimeters). 49.6, 49.6, 49.6, 49.7, 49.6, 49.5, 49.4, 49.7, 49.6

How would you express the length of this rod ?

[ ( 49.6 0.1) cm ]

27. Determine the percentage error for each of the following quantities : (a) 12.21 0.01cm (b) 1.26 0.005 mm (c) 42.8 0.2 g [0.08%, 0.4%, 0.5%] 28. The dimensions of x and y are found to be 8.46 0.02cm and 3.22 0.01cm respectively. Determine the probable error in : (i) x +y (ii) x-y (iii) xy (iv) x/y [ (11.68 0.03) cm, (5.24 0.03)cm, (27.2 0.1)cm 2 , ( 2.63 0.01) ] 29. If x = 18.0 0.3m and y = 1.2 0.05m , determine the percentage error in: (i) x 30. If (ii) y (iii) xy (iv) x/y [2%, 4%, 5%, 6%]

r = 9.9 0.1m , determine the percentage error for :(b) r2 (c) r3 [ 1%, 2%, 3% ]

(a) r