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 lightc=3 xx 10^(8)ms^(-1) g=10ms^(-2) and the normal atmospheric pressure P=10^(5) Nm^(-2)

If the velocity of light, acceleration due to gravity and normal press

1.	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 lightc=3 xx 10^(8)ms^(-1) g=10ms^(-2) and the normal atmospheric pressure P=10^(5) Nm^(-2)
Answer» SOLUTION :`[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)`