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Check by dimensional correctness of T=2p...

Check by dimensional correctness of `T=2pisqrt((l)/(g))` for a simple pendulum,
Where, T - time `" "` l - length`" "` g- acceleration due to gravity

Text Solution

Verified by Experts

The dimensional of LHS= the dimension of `T=[M^(0)L^(0)T^(1)]`
The dimension of RHS `=(("dimensions of length")/("dimensions of acceleration "))^(1//2)" "` (`:. 2 pi` is a dimensionless constant )
`((L)/(LT^(-2)))^(1//2)=(T^(2))^(1//2)=[T]=[M^(0)L^(0)T^(1)]`
Since the dimesions are same on both the sides, the relation is correct.
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