Question

HEYA !!

QUESTION :

If force, velocity and time are taken as fundamental quantities.

What would be dimension of work.

Answer 1

Force = m×a

m = mass
a = acceleration

W = F× S. ------------------- (I)
S= displacement

Change of rate with respect time and velocity

V = S / t
S = V × t

from equation (I)

[ W = F ×V × t ] N×m

W = work ( Jule)
F = Force ( Nuton)
V = Velocity ( m/sec)
t = Time. (sec)

this formula, dimension formula of the work when force, time and velocity are taken as fundamental quantities.

================

I hope it's help you....!! :) ✌️✌️

Answer 2

Thanks for your question !

        Work will be force and displacement's product. Thus, W = F × s. Where, W is work, F is force and s is displacement done.

        We know that, v = s/t. *(above units will be as it is including v = velocity and t = time)

        Therefore the distance has its dimensions.  Where, we come to know important units are - time × velocity. That is, t × v.

        Hence, the answer is - Dimensions of work done here are F v t. Where, F is force. v is velocity and t is time.