Physical quantities and units

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Question

In an ancient civilization, the unit of length was half of meter, the unit of mass was double the kilogram and the unit of time was half of second. The ratio of joule and the new unit of energy is _________

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Solution

Unit of Energy, 1 J $= k g m^{2} s^{- 2}$ (old unit)
Now, according to question
New unit of mass $= a = 2 k g$
New unit of length $= b = \frac{1}{2} m$
New unit of time $= c = \frac{1}{2} s$
New unit of energy $= a b^{2} c^{- 2}$
Ratio $=$ $\frac{New unit}{Old unit} = \frac{a b^{2} c^{- 2}}{k g m^{2} s^{- 2}} = (\frac{2 k g}{k g}) {(\frac{\frac{1}{2} m}{m})}^{2} {(\frac{\frac{1}{2} s}{s})}^{- 2} = 2$

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Physical quantities and units

Remember concepts with our Masterclasses.

In an ancient civilization, the unit of length was half of meter, the unit of mass was double the kilogram and the unit of time was half of second. The ratio of joule and the new unit of energy is _________

Unit of Energy, 1 J =kgm2s-2 (old unit)Now, according to questionNew unit of mass =a=2kgNew unit of length =b=12mNew unit of time =c=12sNew unit of energy =ab2c-2Ratio =New unitOld unit=ab2c-2kgm2s-2=2kgkg12mm212ss-2=2

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