Question

if force(F), acceleration (A),and time(T) are fundamental units ,then dimensions of work is​

Answer 1

In a system of units if force (F), acceleration (A) and time (T) are taken as fundamental units, then the dimensional formula of energy is: FA2T.

Answer 2

Answer:

if force(F), acceleration (A),and time(T) are fundamental units ,then dimensions of work is done by following method...

$[F]=[M][L][T] ^{2}$  

$[A]=[L][T] ^{2}$

T=T

Energy = work = force * displacement

$M][L]^{2} [T]^{2} =[F] ^{2} [A] ^{2} [T] ^{2}$

$=[M][L] ^{2} [T] ^{2} =[[M][L][T] ^{2} ] a [[L][T] ^{2} ] b [T] c$

power of [M]=a⇒a=1

power of [L]=a+b=2⇒b=1

power of [T]=−2=−2a−2b+c⇒c=2

So energy =$[F][A][T] ^{2}$

Explanation:

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