2. d. 29 cm = ? in e. 12 mi h -1 = ? m s -1

6. Determine a dimension and the S.I. unit for the following quantities: a. Velocity b. Acceleration c. Linear momentum d. Density e. Force Solution : a. The S.I. unit of velocity is m s  1 . Example 1.2 : or

7. b. Its unit is m s  2 . d. S.I. unit : kg m  3 . c. S.I. unit : kg m s  1 . e. S.I. unit : kg m s  2 .

8. Determine Whether the following expressions are dimensionally correct or not. a. where s , u , a and t represent the displacement, initial velocity, acceleration and the time of an object respectively. b. where t , u , v and g represent the time, initial velocity, final velocity and the gravitational acceleration respectively. c. where f , l and g represent the frequency of a simple pendulum , length of the simple pendulum and the gravitational acceleration respectively. Example 1.3 :

9. Solution : a. Dimension on the LHS : Dimension on the RHS : Dimension on the LHS = dimension on the RHS Hence the equation above is homogeneous or dimensionally correct. b. Dimension on the LHS : Dimension on the RHS : Thus Therefore the equation above is not homogeneous or dimensionally incorrect. and and

10. Solution : c. Dimension on the LHS : Dimension on the RHS : Therefore the equation above is homogeneous or dimensionally correct.

11. The period, T of a simple pendulum depends on its length l , acceleration due to gravity, g and mass, m . By using dimensional analysis, obtain an equation for period of the simple pendulum. Solution : Suppose that : Then where k , x , y and z are dimensionless constants. Example 1.4 : ………………… (1)

12. By equating the indices on the left and right sides of the equation, thus By substituting eq. (3) into eq. (2), thus Replace the value of x , y and z in eq. (1), therefore The value of k can be determined experimentally. ………………… (2) ………………… (3)

13. Determine the unit of  in term of basic unit by using the equation below: where P i and P o are pressures of the air bubble and R is the radius of the bubble. Solution : Example 1.5 :

14. Since thus Therefore the unit of  is kg s -2