If the units of mass, length and time are 1000 lb , 3 ft, 60 s respectively, then find the unit of work.

Solution

Work = Force

cross times

distance
So, dimensional formula of work is,

straight W space equals open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 2 end exponent close square brackets

Therefore unit of work is given by,

u =1000lb x (3ft) x (60s)^-2

equals fraction numerator 1000 cross times 9 over denominator open parentheses 60 close parentheses squared end fraction fraction numerator lb. ft squared over denominator straight s squared end fraction equals space 2.5 lb. ft squared divided by straight s squared

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