if length, time and energy are fundamental units find the dimension of mass - Physics - Units And Measurements

Question

if length, time and energy are fundamental units find the dimension
of mass

Pintu B. · Accepted Answer

Dear Student ,
Here in this case let mass be proportional to length , time and
energy
So , M = Ealbtc
Now , [E] = [ ML2T-2 ] , [l] = [ L
] , [ t ] = [T ]
So , M1L0T0=ML2T-2aLbTc⇒M1L0T0=MaL2a+bT-2a+cEquating LHS and RHS we get ,a=1 ,2a+b=0⇒2+b=0⇒b=-2,-2a+c=0⇒-2+c=0⇒c=2Putting the values of a,b,c we get ,M=EL-2T2
Hope this helps you
Regards