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fpressure P, velocity v and time Tare taken as the fundamental (base) quantities, Jind the dimensional formula of Jorce. |
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Answer» Solution :Let FORCE = F= `P^(a)V^(b)T^(c )` `(F)= M^(1)L^(1)T^(-2), (P) = M^(1)L^(-1)T^(-2)` `(V) = M^(0)L^(1)T^(-1), (T)= M^(0)L^(0)T^(-1)` `:. MLT^(-2)= (ML^(-1)T^(-2))^(a)(M^(0)L^(0)T^(-1))^(b)(M^(0)L^(0)T^(1))^(c)` `MLT^(-2) = M^(a)L^(-a+b)T^(-2a+b+c)` `:.` Comparing powers of M,L,T on both sides a=1 , -a+b=1 `:.` b=2 and `-2a-b +c =-2 , -2 -2+c=-2,c=2` `:.` Force (F) = `PV^(2)T^(2)`. |
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