1.

Show dimensionally that the relation `t = 2pi((I)/(g))` is incorrect, where I is length and t is time period of a simple pendulum , g is acc. Due to gravity. Find the correct form of the relation, dimensionally

Answer» `RHS = 2pi((I)/(g)) = (L)/(LT^(-2))`
`=T^2 != t(LHS)`
:. Formula is incorrect
Let `t =k l^a g^b …..(i)`
`[M^0L^0T^1] = L^a (LT^(-2))^b = L^(a +b) T^(-2b)`
Using principle of homogeneity of dimensions,
` a +b =0, -2b =1, b = -(1)/(2)`
`:. a =-b =- (-(1)/(2)) = (1)/(2)`
From (i), `t = kl^(1//2) g^(-1//2) = k sqrt((I)/(g))`


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