The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)^(n) and (average velocity of the liquid)^(m) . Which of the following relations between m and n is correct?

Options

A. `m=n`
B. `m=-n`
C. `m^(2)=n`
D. `m=-n^(2)`

Answer

B

Explanation

Let `M=p^(n)v^(m)`
`ML^(-2)T^(-1)=(ML^(-1)T^(-2))^(n)(LT^(-1))^(m)`
`=M^(n)L^(-n+m)T^(-2n-m)`
`therefore" "n=1, -n+m=-2`
`therefore" "m=-2+n=-2+1=-1" "therefore" "m=-n`