If the unit of force is 1 ,kN,the unit of len | vedclass

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Question

(A) The dimensional formula for force is $[F] = [M L T^{-2}]$.Given units are: Force $F' = 1 \,kN = 10^3 \,N$,Length $L' = 1 \,km = 10^3 \,m$,and Time

Vedclass · Accepted Answer

$10000$

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(A) The dimensional formula for force is $[F] = [M L T^{-2}]$.Given units are: Force $F' = 1 \,kN = 10^3 \,N$,Length $L' = 1 \,km = 10^3 \,m$,and Time $T' = 100 \,s$.We know that $F = M L T^{-2}$,so $M = F L^{-1} T^2$.Substituting the given units into the formula for mass:$M' = F' \cdot (L')^{-1} \cdot (T')^2$$M' = (10^3 \,N) \cdot (10^3 \,m)^{-1} \cdot (100 \,s)^2$$M' = 10^3 \cdot 10^{-3} \cdot (10^2)^2 \,kg$$M' = 1 \cdot 10^4 \,kg = 10000 \,kg$.Therefore,the unit of mass is $10000 \,kg$.

If the unit of force is $1 \,kN$,the unit of length is $1 \,km$,and the unit of time is $100 \,s$,what will be the unit of mass in $kg$?

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