Question

If force velocity and mass are chosen as fundamental quantities then the dimension of length in terms of these quantities will be

Answer 1

Answer:

Dimension of Length is $F^{-1}v^2m^1$

Explanation:

Given:

Force, velocity and mass are fundamental quantities.

To calculate: Dimension of Length in terms of given quantities.

The dimension of force is $MLT^{-2}$

The dimension of velocity is $LT^{-1}$

The dimension of mass is $M$

The dimension of length is $L$

Let Length varies as

$l\propto F^av_bm^c\\\\L=(MLT^{-2})^a(LT^{-1})^bM^c$

By comparing we have

a=-1

b=2

c=1

Dimension of Length is $F^{-1}v^2m^1$

Answer 2

Given:

Basic quantities = Force, Mass and Velocity

To Find: Dimension of Length in terms of Force, Mass and Velocity.

Calculation:

Let Force, Mass and Velocity be expressed as F, M and V respectively.

Formula for Force:

Force = Mass * Acceleration

$F=M*LT^{-2} \\T^{-2}=FM^{-1} L^{-1}$   ---------------- (i)

Formula for velocity:

$Velocity =\frac{distance}{time}$

$V=LT^{-1}$

$T=LV^{-1}$    ------------------     (ii)

Substituting value of T from (ii)  in (i):

$L^{-2} V^{2} =FM^{-1} L^{-1} \\L^{-1} =FV^{-2} M^{-1} \\L=F^{-1} V^{2} M$

Answer:

Dimension of length is $F^{-1} V^{2} M$.