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Check the correctness of the relation T=...

Check the correctness of the relation `T=2pisqrt((l)/(g))`, where `T` is the time period, l is the length of pendulum and g is acceleration due to gravity.

Text Solution

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Step 1 : Dimensional formula of Time `[T]=T`, length `[l]=L`, Acceleration due to gravity `[g]=LT^(-2)` and `2pi` is a dimensionless constant.
Step 2 : Now `[2pisqrt((l)/(g))]=[(L)/(LT^(-2))]^(1//2)=[T^(2)]^(1//2)impliesM^(0)L^(0)T`. Also `[T]=M^(0)L^(0)T`
Step 3 : Since the dimensions of R.H.S are equal to dimensions of L.H.S . So the relation is dimensionally correct.
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