Question bank — SI units — seven base units and all derived units

Kilogram woh ek SI base unit hai jiske naam mein prefix hai. ::: Sahi — "kilo" mass ki base unit mein baka hua hai, metre ya second ki tarah nahin jo prefix-free hain; yeh ek historical accident hai, logical rule nahin. Kisi quantity ke units ho sakte hain phir bhi woh dimensionless ho sakti hai. ::: Sahi — angle in radians, metre/metre hai, ek pure ratio; woh dimensionless hai phir bhi hum "rad" likhte hain yeh signal karne ke liye ki yeh ek angle hai. Do quantities jinki same base-unit form hai woh same physical quantity honi chahiye. ::: Galat — torque aur energy dono ${\text{kg⋅m}}^2{\text{s}}^{-2}$ hain phir bhi ek rotational effect hai aur doosra work hai; identical dimensions identical meaning force nahin karte. Frequency (Hz), radioactivity (Bq) aur angular frequency sab ${\text{s}}^{-1}$ reduce ho jaati hain. ::: Base units mein sahi — lekin dhyan raho angular frequency $\omega$ conventionally $\text{rad/s}$ likhi jaati hai (radian ek dimensionless naam hai), aur $\omega =2\pi f$, isliye $1\text{Hz}$ spin $2\pi \text{rad/s}$ hai chahe dono ${\text{s}}^{-1}$ tak strip down ho jaayein. Angular frequency in rad/s, frequency in Hz ke barabar hoti hai. ::: Galat — dono mein $2\pi$ ke factor ka fark hai: $\omega =2\pi f$, kyunki ek full cycle (1 Hz) $2\pi$ radians sweep karta hai; radian "unit" dimensionless hai isliye yeh factor base-unit form mein chhup jaata hai. Mole ek base unit hai chahe woh "sirf ek number" ho ($N_A=6.022\times 10^{23}$). ::: Sahi — amount of substance convention se ek independent base quantity declare ki gayi hai; mole entities count karta hai aur baaki chhe se build nahin kiya ja sakta. Celsius degrees aur kelvin degrees same size ke hain. ::: Sahi — sirf zero point alag hai ($T_{°C}=T_K-273.15$); 1 °C ki rise 1 K ki rise ke barabar hai, isliye temperature differences numerically identical hain. Kyunki $c$ (speed of light) ab ek fixed exact number hai, ise aur carefully measure karne se iska value change ho sakta hai. ::: Galat — 2019 redefinition ke baad $c$ defined exact hai; better experiments ab metre ko refine karte hain, $c$ ko nahin. Litre ek SI unit hai. ::: Galat — litre ek accepted non-SI unit hai; coherent SI volume unit cubic metre hai ($1\text{L}=10^{-3}{\text{m}}^3$), aur litre sirf convenience ke liye tolerate ki jaati hai.

"Force mechanics mein itni fundamental hai ki newton ek base unit honi chahiye." ::: Error — force $F$ derived hai $F=ma$ (mass times acceleration) se, isliye iska unit ${\text{kg⋅m⋅s}}^{-2}$ mass, length aur time se banta hai; mechanics ka base set sirf yeh teen hain. "Weight aur mass dono kilograms mein measure hote hain." ::: Error — mass kilograms mein hai, lekin weight ek force hai jo newtons mein measure hoti hai; inhe confuse karna ek base quantity ko derived ke saath mix karta hai. "°C ek SI base unit hai kyunki temperature ek base quantity hai." ::: Error — temperature ki base unit kelvin hai; Celsius ek shifted convenience scale hai jo ussi se derive hui hai, base unit nahin. "Gram SI base unit hai; kilogram sirf 1000 grams hai." ::: Error — officially kilogram (prefix included) base unit hai; gram usi se define hota hai, ulta nahin. "Pressure force hai, isliye iska unit newton hai." ::: Error — pressure force per area hai, isliye pascal ${\text{N/m}}^2={\text{kg⋅m}}^{-1}{\text{s}}^{-2}$ hai; area se divide karne par dimensions badal jaate hain. "Electrons ka ek mole aur electrons ka ek kilogram same amount of stuff describe karte hain." ::: Error — mole particles count karta hai jabki kilogram inertia/mass measure karta hai; yeh alag base quantities hain jo alag sawaalon ke jawaab deti hain. "$E=m{c}^2$ dimensionally sahi nahin ho sakta kyunki energy mass ke barabar nahin honi chahiye." ::: Error — $E$ energy, $m$ mass, $c$ speed of light ke saath, check kaam karta hai: $[m{c}^2]=\text{kg}\cdot (\text{m/s}{)}^2={\text{kg⋅m}}^2{\text{s}}^{-2}=\text{J}$, bilkul energy; constant $c^2$ missing dimensions carry karta hai. "Kilometre aur kilogram dono par prefix ka matlab dono 1000 base units hain." ::: Error — kilometre $1000$ metres hai (base unit metre), lekin kilogram khud base unit hai; tum iske upar aur prefix nahin laga sakte, isliye "kilo-kilogram" tonne (Mg) hai, base unit nahin. "Tum $\mu \text{k}$ (microkilo) likh sakte ho milli ki jagah." ::: Error — SI compound prefixes forbid karta hai; sirf ek prefix ek waqt mein kisi unit se attach ho sakta hai, isliye milli (m) likhna zaroori hai, micro-kilo kabhi nahin.

2019 mein base units ko physical objects ki jagah constants of nature se kyun redefine kiya gaya? ::: Objects drift karte hain, scratch hote hain, aur kho sakte hain (purana kilogram cylinder actually mass change kar gaya tha); kisi constant of nature ko fix karna ek aisa standard deta hai jo kabhi vary nahin karta aur kisi bhi lab mein reproducible hai. Luminous intensity (candela) ek base quantity kyun hai jabki yeh power ka ek form lagti hai? ::: Candela human eye ki alag wavelengths par response se weighted hoti hai, isliye ise raw watts tak reduce nahin kiya ja sakta; woh human-centred weighting ise itna independent banata hai ki ise base declare kiya gaya. Temperature ko energy se kyun nahin banaya ja sakta, chahe heat aur energy linked lagte hain? ::: Link ke liye Boltzmann constant $k$ ki zaroorat hai energy ko temperature mein convert karne ke liye; temperature ko independent declare karne se $k$ translating karta hai, kelvin ko derived energy unit force karne ki jagah. Derived units (newton, joule) ko naam kyun dete hain instead of hamesha base units likhne ke? ::: Named units lambi strings jaise ${\text{kg⋅m}}^2{\text{s}}^{-2}$ ko ek word mein compress karte hain, equations readable banate hain — lekin tum hamesha unhe base units mein unfold kar sakte ho dimensions check karne ke liye. Ek pure number jaise $\frac{1}{2}$ ko unit check mein kyun ignore kiya jaata hai? ::: Dimensionless constants koi units carry nahin karte, isliye woh base-unit form change nahin kar sakte; sirf woh quantities jo dimensions ke saath hain unit determine karti hain. Saat base quantities dimensionally independent kyun honi chahiye? ::: Agar ek ko doosron se likha ja sakta to woh redundant hoti — tumhare paas zaroorat se zyada standards hote; independence ek minimal, non-overlapping "basis" guarantee karta hai saare measurements ke liye. Agar electronvolt (eV) SI unit nahin hai to physics mein kyun allow hai? ::: Yeh ek tolerated non-SI unit hai jo atomic energies ke size ki hai ($1\text{eV}=1.602\times 10^{-19}\text{J}$); yeh convenient hai lekin SI equations mein coherently fit hone ke liye joules mein convert karna padta hai.

Kisi truly dimensionless quantity ki base-unit form kya hoti hai, jaise refractive index ya strain? ::: Uske koi base units nahin hote — refractive index speeds ka ratio hai aur strain length/length hai, isliye har base unit cancel ho jaati hai aur answer $1$ (pure number) hota hai; figure mein amber "1" dekho. Kya same units lekin alag meanings wali do quantities (jaise torque + energy) add karna physically sense karta hai? ::: Nahin — chahe dono ${\text{kg⋅m}}^2{\text{s}}^{-2}$ hain, physics rotational torque ko energy mein add karna forbid karta hai; matching units zaroori hai lekin valid sum ke liye kaafi nahin hai. Agar koi formula $\sin$ ya $e^x$ jaisi function ko dimensionless argument deta hai, yeh tumhe kya bata hai? ::: Aisi functions dimensionless inputs demand karti hain, isliye argument ke units cancel hone chahiye; agar nahin hote, formula galat hai — yeh ek powerful consistency check hai. Absolute zero (0 K) par Celsius reading kya hoti hai, aur kya 0 K reachable hai? ::: $0\text{K}=-273.15\text{°C}$; yeh temperature ki theoretical floor hai lekin third law of thermodynamics kehta hai ise approach kiya ja sakta hai, exactly reach nahin kiya ja sakta. Kya koi derived unit kabhi "base unit ban" sakta hai? ::: Principle mein yeh choice ki kaunsi quantities base hain ek convention hai — SI force ko base aur mass ko derived choose kar sakta tha; current saat practicality ke liye chosen hain, is liye nahin ki woh uniquely fundamental hain. Kya angular measure (radian) ek base unit hai, derived unit hai, ya kuch aur? ::: Aam sense mein dono nahin — radian ek dimensionless derived unit hai, arc length over radius (metre/metre) se define kiya gaya, isliye iska naam hai lekin koi dimensions nahin hain. Steradian kahan fit hota hai — aur yeh radian se alag kaise hai? ::: Radian jaisi hi category: ek dimensionless named derived unit, lekin solid angle ke liye, sphere par area over radius-squared (${\text{m}}^2/{\text{m}}^2$) se define kiya gaya; dono ke naam hain phir bhi base units mein vanish ho jaate hain. Kisi quantity ko zeroth power tak raise karne par unit kya hoti hai, jaise $v^0$? ::: Woh dimensionless hai ($=1$); koi bhi unit zero power par khud ko cancel kar deti hai, aur koi base units nahin wala pure number reh jaata hai. Kya minute, hour, tonne aur bar SI ka hissa hain? ::: Nahin — yeh SI ke saath use ke liye accepted hain lekin non-coherent hain: minute/hour ($60\text{s}$, $3600\text{s}$), tonne ($10^3\text{kg}$), bar ($10^5\text{Pa}$); ek "coherent" unit apni defining equation se exactly $1$ ke conversion factor ke saath aati hai, isliye second, kilogram aur pascal prefer kiye jaate hain. Derived unit ke liye "coherent" ka kya matlab hai? ::: Ek coherent unit apni defining equation se exactly $1$ ke conversion factor ke saath aati hai (jaise $1\text{N}=1{\text{kg⋅m⋅s}}^{-2}$); litre ya bar jaisi units non-coherent hain kyunki ek power-of-ten factor andar ghus jaata hai.