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{:(,"Column I",,"Column II",,"Column III...

`{:(,"Column I",,"Column II",,"Column III",,"Column IV"),(,"Physical quantity",,"MKS system",,"CGS system",,"FPS system"),((A),"Length",(a),"newton",(p),"erg",(1),"poundal"),((B),"Mass",(b),m,(q),"dyne",(2),"ft-poundal"),((C),"Force",(c),kg,(r),erg//s,(3),ft),((D),"Power",(d),"joule",(s),g,(4),lb),((E),"Work",(e),"watt",(t),cm,(5),"ft-poundal"//s):}`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to match the physical quantities with their respective units in the MKS (Meter-Kilogram-Second), CGS (Centimeter-Gram-Second), and FPS (Foot-Pound-Second) systems. We will go through each physical quantity one by one. ### Step-by-Step Solution: 1. **Identify the Physical Quantity A: Length** - In the MKS system, the unit of length is **meter (m)**. - In the CGS system, the unit of length is **centimeter (cm)**. - In the FPS system, the unit of length is **foot (ft)**. - Therefore, for A (Length), we have: - MKS: **m** (not listed in options) - CGS: **cm** (option t) - FPS: **ft** (option 3) - **Match:** A → (t, 3) 2. **Identify the Physical Quantity B: Mass** - In the MKS system, the unit of mass is **kilogram (kg)**. - In the CGS system, the unit of mass is **gram (g)**. - In the FPS system, the unit of mass is **pound (lb)**. - Therefore, for B (Mass), we have: - MKS: **kg** (option c) - CGS: **g** (option s) - FPS: **lb** (option 4) - **Match:** B → (c, s, 4) 3. **Identify the Physical Quantity C: Force** - In the MKS system, the unit of force is **Newton (N)**. - In the CGS system, the unit of force is **dyne**. - In the FPS system, the unit of force is **poundal**. - Therefore, for C (Force), we have: - MKS: **N** (option a) - CGS: **dyne** (option q) - FPS: **poundal** (option 1) - **Match:** C → (a, q, 1) 4. **Identify the Physical Quantity D: Power** - In the MKS system, the unit of power is **watt (W)**. - In the CGS system, the unit of power is **erg/second**. - In the FPS system, the unit of power is **foot-poundal/second**. - Therefore, for D (Power), we have: - MKS: **W** (not listed in options) - CGS: **erg/s** (option r) - FPS: **foot-poundal/s** (option 5) - **Match:** D → (r, 5) 5. **Identify the Physical Quantity E: Work** - In the MKS system, the unit of work is **joule (J)**. - In the CGS system, the unit of work is **erg**. - In the FPS system, the unit of work is **foot-poundal**. - Therefore, for E (Work), we have: - MKS: **J** (option d) - CGS: **erg** (option p) - FPS: **foot-poundal** (option 2) - **Match:** E → (d, p, 2) ### Final Matches: - A → (t, 3) - B → (c, s, 4) - C → (a, q, 1) - D → (r, 5) - E → (d, p, 2)
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