DHS 01 Measurements (Tutorial Solutions)

Dunman High School H2 Physics 2024/2025 1 TOPIC 1: MEASUREMENT TUTORIAL Suggested Answers 1 (a) Derived quantities Definition Defining Equation Derived units (base) Alternative unit(s) Area The extent of a two- D figure or shape in a plane. l π = × = rectangle 2 circle Aw Ar m2 - Moment Moment of a force about a point is the product of the magnitude of the force and the perpendicular distance of the force from the point. ⊥= ×moment of a force Fd kg m2 s-2 N m Pressure Force per unit area. = Fp A kg m-1 s-2 N m-2 , Pa Work done Force × Displacement in direction of force θ=W cosFd kg m2 s-2 J Power Work done per unit time. = WP t kg m2 s-3 J s-1 , W Resistance The ratio of potential difference across the conductor to the current flowing in it. I= VR kg m2 s-3 A-2 V A-1, Ω 1(b) ( ) = ⇒= = = = = = -1 2 -2 2 -1 Units of JUnits of J sUnits of s Base units of kg m s s kg m s E hf Eh f Eh f h Common mistake: Students often incorrectly equate physical quantity with units in the working, for example, by writing: h = kg m2 s−1, which is an incorrect equation. ( ) ( ) = = = = = = -2 2 -2 -1 -12 -2 2 -3 -1 1 kg m s m1 J 1 Nm1 V 1 kg m s C1 C 1 C 1 C 1 kg m s A s 1 kg m s A

Dunman High School H2 Physics 2024/2025 2 2. ( )( )( )( ) 2 2 3 2 22 2 2 base units of base units of 1base units of 2 kg m s 1 kg m m m s kg m s 1kg m s D FC Avρ − −− − − = = = = Hence, CD has no units. It is dimensionless. 3. A homogeneous equation is one in which every term has the same units. To determine whether an equation is homogeneous, find the units of each term and compare. If the units are the same, the equation is homogeneous. Unit of v = m s −1. (A) ( ) ( ) 2 2 2 -1Units of m s m m s m s vg g λ λ −− = = = = Comparing units of v and λg , we conclude that the equation λ=vg is homogeneous. (B) 2 21m sUnits of s s gv h g hm − −− = = = = Comparing units of v and g h , we conclude that the equation = gv h is not homogeneous. (C) ( )( ) ( ) 11 3 2 12 122Units of kg m m s m kg m s kg m s v gh gh ρ ρ −− − −− − = = = = Comparing units of v and ρgh , we conclude that the equation ρ=v gh is not homogeneous. (D) 12 142 212 3 m sUnits of kg m s kg m sk g m gv g ρ ρ − −−− − − = = = = Comparing units of v and ρ g , we conclude that the equation ρ= gv is not homogeneous.

Dunman High School H2 Physics 2024/2025 3 4. (i) Pressure is defined as = force areaP . Base unit of pressure P = Base unit of 2 12 2 force kg m s kg m sarea m − −−= = (ii) 12 2 2 1 3 kg m sUnits of m s m skg m Pc γ ρ −− −− −= = = = (iii) c could be velocity or speed. 5. ρρ++ = 21 2p hg v k (i) ( ) ( ) ( )( ) ( )( ) 2 2 12 3 2 12