Question

If velocity,force,time are taken as fundamental units find the dimension of pressure velocity,force and time is taken as fundamental units then find the dimension of Pressure

Answer 1

Answer:

☑ fundamenatal units of dimensions

Length = [L]

Mass = [M]

Time = [T]

➡

☑ As a given,

Dimensions of force are

force = mass X acceleration = M X [LT^(-2)]

= MLT^(-2)

☑ dimensions of a

Velocity = [L (T)^-1]

Force = [M L (T )^(-2)]

Time = [T]

☑ Force = m. a

we know,

☑ but Take velocity, time and force as a fundamental units...... so

☑ velocity = distance / time

distance take it as length [L]

Distance[length] = Velocity X time

squaring both the side

(length) ^2 = ( Velocity X time) ^2

= (Velocity )^2. (time) ^2

(L )^2 = V^(2) . (T) ^2

☑ [dimensions of area are A = (L^(2))]

pressure = force/ Area

= [ (F) / (A) ]

⚫ pressure = [ (F) / [(V)^2 . (T) ^2]

= [ [F . V^(-2) . (T) ^(-2)]

Answer 2

If force is fundamental unit then it's dimension is F

Velocity would have dimension V

and Time has T

Pressure=Force /Area

length=velocity×time.so dimension of length is ,[L]=[VT]

Dimensions of area is ,[L^2]=[V^2T^2]

so dimensions of pressure=force /area

$f \div (v^{2}t ^{2} ) = f v ^{ - 2} t ^{ - 2}$