Question

Mechanical power is represented by

P =Fv + Av^3 where, F is the force, v is the

velocity, A is the area and p is the density.

a) The dimensional formula of power

is............

b) Check the dimensional validity of the

above equation.

Answer 1

so the given P=FV+AV^3

THE FORMULA FOR F= MLT^-2 (ma)

V=LT^-1 (DISTANCE/TIME)

a= l*b(L^2)

A) THE DIMENSIONAL FORMULA OF POWER IS

FORMULA =FORCE/AREA

SO MLT^-2/L^2 =ML^-1T^-2

here if we want to add two variables say 3x +4x here only if x is the same variable we can add so the dimension of fv must be equal to av^3 suppose if they ask u 2 find the dimension of some constant by giving some equation plz keep ths idea in ur mind

b) p=ML^-1T^-2 in Lhs and in rhs

fv =( MLT^-2) (LT^-1)=ML^T^-3

AV^3= (L^2) (LT^-1)^3=L^5T^-3

so c here acc to the idea i said before only if de dimensions of all the 3 quantities we can say that they are dimensionally crt so here it is not dimensionally valid

Answer 2

Answer:

Explanation:

Power=work/time=force*displacement/time

Power=M1 L1 T-2*L1/T1

Power=M1L1+1T-2-1=M1L2T-3