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Question

Physics Question on Units and measurement

Imagine a system of units in which the unit of mass is 10 kg10\, kg, length is 1 km1 \,km and time is 1 min1 \,min. Then 1 joule in this system is equal to

A

360360

B

3.6×10−43.6\times10^{-4}

C

3.6×1043.6\times10^{4}

D

3.63.6

Answer

3.6×10−43.6\times10^{-4}

Explanation

Solution

n1u1=n2u2n_{1}u_{1}=n_{2}u_{2} ⇒n2(n1n2)u1=(M1M2)1(L1L2)2(T1T2)−2\Rightarrow{ n _{2}}\left(\frac{n_{1}}{n_{2}}\right)u_{1}=\left(\frac{M_{1}}{M_{2}}\right)^{^1}\left(\frac{L_{1}}{L_{2}}\right)^{^2}\left(\frac{T_{1}}{T_{2}}\right)^{^{-2}} u1=(1 kg10 kg)(1 m1 km)2(1 s1 min)−2×1u_{1}=\left(\frac{1\,kg}{10\,kg}\right)\left(\frac{1\,m}{1\,km}\right)^{2}\left(\frac{1\,s}{1\,min}\right)^{-2}\times1 =110×10−6×60×60=\frac{1}{10}\times10^{-6}\times60\times60 =36×10−5=36\times10^{-5} =3.6×10−4=3.6\times10^{-4}