If the velocity of light, acceleration due to gravity and normal pressure are chosen as fundamental units, find the unit of mass, length and time. Given that velocity of light `c=3 xx 10^(8)ms^(-1) g=10ms^(-2)` and the normal atmospheric pressure `P=10^(5) Nm^(-2)`

Explanation

`[c]=L^(1)T^(-1)=3xx10^(8)ms^(-1) .....(1)`
`[g]=L^(1)T^(-2) == 10 ms^(-2) .....(2)`
`[P]=M^(1)L^(-1)T^(-2)=10^(5)Nm^(-2) ....(3)`
Now, we.ll find out value of M,L, & T.
`:.(L^(1)T^(-1))/(L^(1)T^(-2))=([C])/([g])=(3xx0^(8))/(10)`
`:.T^(1)=3xx10^(7)s...(i)`
Now `[C]=(L^(1))/(T^(1)) rArr L^(1)=[C]xxT^(1)`
`=3xx10^(8)xx10^(15)m...(ii)`
`[P]M^(1)xxL^(-1)T^(-2)=10^(5)`
`:.M^(1)=([P])/(L^(-1)T^(-2))=[P]L^(1)T^(2)`
`=10^(5)xx9xx10^(15)xx9xx10^(14)` (From equatio (i), (ii))
`:. M^(1)=81xx10^(34) kg (ii)`