If velocity, time and force were chosen the basic quantities, find the dimensions of mass?
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M^1 1L^0T^0
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[mass] = K[velocity]^a [time ]^b[force] ^c
we know
[ velocity ] =[LT^-1]
[time ] =[ T]
[force ] =[MLT^-2]
[mass]= [M]
now ,
[M] =k [LT^-1]^a [T]^b [MLT^-2]^c
=k [L]^(a+c) [M]^c [T]^(-a+b-2c)]
compare both side
c=1
a+c=0 => a= -c = -1
-a-2c+b=0 => b=a+2c =1
hence ,
mass =k (time )(force) / (velocity)
we know
[ velocity ] =[LT^-1]
[time ] =[ T]
[force ] =[MLT^-2]
[mass]= [M]
now ,
[M] =k [LT^-1]^a [T]^b [MLT^-2]^c
=k [L]^(a+c) [M]^c [T]^(-a+b-2c)]
compare both side
c=1
a+c=0 => a= -c = -1
-a-2c+b=0 => b=a+2c =1
hence ,
mass =k (time )(force) / (velocity)
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