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 :
![Basic quantity is defined as a quantity which cannot be derived from any physical quantities ,[object Object],[object Object],cd candela Luminous Intensity mol mole N Amount of substance A ampere I Electric current K kelvin T/ Temperature s second t Time kg kilogram m Mass m metre l Length Symbol SI Unit Symbol Quantity](https://image.slidesharecdn.com/c1h2-110414010207-phpapp01/85/C1h2-1-320.jpg)
