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Show that the expression of the time per...

Show that the expression of the time period T of a simple pendulum of length l given by `T = 2pi sqrt((l)/(g))` is dimensionally correct

Text Solution

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The dimensions of LHS= the dimention of `T=[M^(0)L^(0) T^(1)]`
The dimensions of RHS`=(("dimensions of length")/("dimensions of acceleration"))^(1//2)" "( :' 2pi "is a dimensionless constant")`
`=[L/(LT^(-2))]^(1//2)=[T^(2)]^(1//2)=[T]=[M^(0) L^(0) T^(1)]`
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