If velocity, force and time are taken as the fundamental quantities, then using dimensional analysis choose the correct dimensional formula for mass among the following. [K is a dimensionless constant]
Text Solution
Verified by ExpertsA
Q = K v -l F T
Let the quantity be Q, then,
Q = f(v,F,T)
Assuming that the function is the product of power functions of v, F and T,
Q = Kv x F y T z ... (i)
where K is a dimensionless constant of proportionality. The above equation dimensionally becomes
[Q] = [LT -1 ] x [MLT -2 ] y [T] z
i.e., [Q] = [M y L (x+y) T (-x-2y+z) ],Now
Q = mass i.e., [Q] = [M]
So Equation (ii) becomes
[M] = [M y +L (x+y) T (-x-2y+z) ]
its dimensional correctness requires
y = 1, x + y = 0 and - x - 2y + z = 0
which on solving yields
x = - 1, y = 1 and z = 1
Substituting it in Equation (i), we get
Q =Kv -1 FT
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