Question

the force of a physical system is given by the expression K*P^a*V^b*T^c where K is dimensionless, V is the velocity and T is time. Find the value of a, b, and c

Answer 1

F=KP^aV^bT^c\\ [F]=[P]^a[V]^b[T]^c\\ [MLT^{-2}]=[ML^{-1}T^{-2}]^a[LT^{-1}]^b[T]^c\\a=1\\1=-1(1)+b\to b=2\\-2=-2(1)-1(2)+c\to c=2