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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

Verified by Experts

The dimensions of LHS `=` the dimension of
`T=[M^(0)L^(0)T^(1)]`
The dimensions of RHS
`=(("dimensions of length ")/("dimensions of acceleration "))^(1//2)` ( `:' 2pi` is a dimensionless const.)
`=((L)/(LT^(-2)))^(1//2)=(T^(2))^(1//2)=[T]=[M^(0)L^(0)T^(1)]`
Since the dimensions are same on both the sides, the relation is correct.
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