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Check the accuracy of the relation T=2pi...

Check the accuracy of the relation `T=2pisqrt((L)/(g))` for a simple pendulum using dimensional analysis.

Text Solution

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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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