Question

Check correctness of equation T=2π√l/g

Answer 1

We prove this equation dimensionally.

Time = (T)

Length = (l)

g means acceleration due to gravity = (lt^-2)

Pi and 2 has no dimension because they are constant.

Now we square both sides we get

T^2 = 4pi^2 (l/g)

T^2 = L/LT^-2

T^2 = L × T^2 / L

T^2 = T^2

HENCE PROVED.

HOPE IT MAY BE HELPFUL FOR YOU. THANKS FOR READING. PLEASE COMMENT

Answer 2

Given that,

The formula as $T=2\pi\sqrt{\dfrac{l}{g}}$

To shows,

The formula is correct or not.

Solution,

It is showed by using dimensional analysis.

$T=2\pi\sqrt{\dfrac{l}{g}}$ ....(1)

Here,

T is time period

l is length of the simple pendulum

g is acceleration due to gravity

Squaring equation (1) such that,

$T^2=\dfrac{4\pi^2l}{g}$

$4\pi^2$ is dimensional less quantity

Dimension of T² = [T²]

Dimension of l is [l]=[L]

Dimension of g is [g]=[LT⁻²]

Taking RHS of equation (1) such that,

$\dfrac{l}{g}=\dfrac{[L]}{[LT^{-2}]}\\\\\dfrac{l}{g}=T^2=LHS$

Hence, proved.

Learn more,

Dimensional analysis

https://brainly.in/question/11761477