Question

16. If Force (F), velocity (V) and acceleration (A) are taken as the fundamental units instead of mass, length and time, express pressure and impulse in terms of F, V and A. *
0/4

Answer 1

Given

Force (F), velocity (V) and acceleration (A) are taken as the fundamental units instead of mass (M), length (L) and time (T).

To find

Express pressure and impulse in terms of F, V and A.

Solution

Pressure

$P=ML^{-1}T^{-2}$

$F=MLT^{-2}$

$V=LT^{-1}$

$A=LT^{-2}$

$P=\alpha F^aV^bA^c\\\Rightarrow ML^{-1}T^{-2}=\alpha (MLT^{-2})^a(LT^{-1})^b(LT^{-2})^c$

Comparing the powers we get

$1=a$

$-1=a+b+c$

$-2=-2a-b-2c$

$-1=1+b+c\\\Rightarrow b=-2-c$

$-2=-2\times 1-(-2-c)-2c\\\Rightarrow c=2$

$b=-2-c=-2-2\\\Rightarrow b=-4$

$\boldsymbol{P=\alpha F^1V^{-4}A^2}$

Impulse

$J=MLT^{-1}$

$J=\alpha F^aV^bA^c\\\Rightarrow MLT^{-1}=\alpha (MLT^{-2})^a(LT^{-1})^b(LT^{-2})^c$

Comparing the powers we get

$a=1$

$1=a+b+c$

$-1=-2a-b-2c$

$1=1+b+c\\\Rightarrow c+b=0\\\Rightarrow c=-b$

$-1=-2a-b-2c\\\Rightarrow -1=-2-b+2b\\\Rightarrow 1=b$

$c=-b=-1$

$\boldsymbol{J=\alpha F^1V^1A^{-1}}$