Question

For the equation f=a^av^bd^c where f is a force . A is area, vis velocity, and d is density. What will be the values of a,b and c on dimensional analysis?

Answer 1

a=-2 b=2 c=-1

force is equal to (M^1L^1T^-2)

area=(L^2)

velocity=(L^1T^-1)

density=(M^1L^-3)

(M^1L^1T^-2)=(L^2 )^a(L^1T^-1)^b(M^1L^-3)

(M^1L^1T^-2)=(L^2a+b-3c) (M^-c) (T^-b)

after solving the equation,

c=-1

b=2

a=-2

{2a+b-3c=1}

{2a=-4}

{a=-2}