NJC 2025 H2 Physics Quantities and Measurement Problem Set

National Junior College Science Department | Physics 1. Quantities & Measurement Problem Set PHYSICAL QUANTITIES AND SI UNITS Guided Exercises For this section of the problem set, you should try the exercises without looking at the guided solutions. The guided solutions are there if you get stuck and you should also use it to understand how to present your work. 1 Perform the following conversion of units: (i) 50 km h-1 to m s-1. [13.9 m s-1] (ii) 320 m s-1 to km h-1. [1152 km h-1] Step-by-step guide Convert km to m and h to min 50 km h-1 = 50 km 1 h = 50 000 𝑚 60 min = 50 000 𝑚 60 ×60 𝑠 = 13.9 m s-1 Convert min to s 320 m s-1 = 320 m 1 s = 320 1000 km 1 60×60 h = 1152 km h-1

National Junior College Science Department | Physics 2 Express the units of the following quantities in SI base units: (i) Gravitational constant G, where 𝐹 = 𝐺𝑀1𝑀2 𝑟2 , 𝐹 is force, 𝑀1 and 𝑀2 are masses and 𝑟 is separation distance between the masses. [m3 kg-1 s-2] (ii)  , if 𝑣 = √ 𝑇 𝜇 where 𝑣 is the speed of the wave on a string of length L held at a tension of T, a type of force. [kg m-1] Look at Examples 1.1 and 1.2 in your lecture notes for a step-by-step guide, it will be useful to rearrange the equations to write G and  in terms of other quantities before determining the units. Please also be mindful of the presentation of your working! (i) 𝐺 = 𝐹𝑟2 𝑀1𝑀2 and 𝐹 = 𝑚𝑎 Units of G = (kg m s−2)(m2) (kg)(kg) = m3 kg-1 s-2 (ii) 𝑣2 = 𝑇 𝜇  𝜇 = 𝑇 𝑣2 and 𝑇 = 𝑚𝑎 Units of 𝜇 = kg m s−2 (m s−1)2 = kg m s−2 m2 s−2 = kg m-1 Presentation style: Always write “units of” in front of the variable you are finding units for. E.g 𝜇 = kg m s−2 (m s−1)2 would be marked wrong for presentation.

National Junior College Science Department | Physics 3 The critical flow speed vc is related to the width a of the obstacle, the density 𝜌 liquid, and its viscosity 𝜂 by one of the equations: (i) vc = 𝐴𝜂𝑎 𝜌 (ii) vc = 𝐵𝜂 𝑎𝜌 (iii) vc = 𝐶𝜌𝑎 𝜂 A, B and C are constants with no units and unit of 𝜂 is Pa s. Determine the correct equation. You are given 3 equations. A dimensionally correct equation is one where the units of each term has the same base units. (pg 8 of your lecture notes) Note that a dimensionally correct equation need not be correct! Hence you can’t actually determine the correct equation, just the dimensionally correct one! Step-by-step guide using (i) Unit of vc = m s-1 Unit of 𝐴𝜂𝑎 𝜌 = 𝑃𝑎 𝑠 (𝑚) (𝑘𝑔 𝑚−3) = (𝑘𝑔𝑚𝑠−2 𝑚2 ) 𝑠 (𝑚) (𝑘𝑔 𝑚−3) = 𝑠−1 (𝑚−3) = 𝑚3𝑠−1 LHS ≠ RHS, (i) is not dimensionally correct Option (ii) is the dimensionally correct equation. 4 Bernoulli’s equation, which applies to fluid flow, states that 𝒑 + ℎ𝜌𝑔 + 1 2 𝜌𝑣2 = 𝑘 Where 𝒑 is a pressure, h a height, 𝜌 a