Question

Prove the correctness of this equation T=2π√L/g

Answer 1

Answer:

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Answer 2

Answer:

To prove:

Correctness of the equation,

$T=\frac{2 \pi \sqrt{L}}{g}$

Proof:

Let us prove by using dimensional analysis.

$\begin{array}{l}{T=M^{0} L^{0} T^{1}} \\ {\frac{\sqrt{L}}{g}=\left[\frac{M^{0} L^{1} T^{0}}{\left(M^{0} L^{1} T^{-2}\right) ]^{\frac{1}{2}}}\right]} \\ {=\left[M^{0} L^{0} T^{2}\right]^{\frac{1}{2}}} \\ {=M^{0} L^{0} T^{1}}\end{array}$

Now we have the dimensional formula for both LHS and RHS

So, now on equating both LHS and RHS of the equation.

We have

$\begin{array}{l}{T=\frac{2 \pi \sqrt{L}}{g}} \\ {M^{0} L^{0} T^{1}=M^{0} L^{0} T^{1}}\end{array}$

LHS = RHS

Hence proved.