Question

check the correctness of equation 1/2mv2=mgh using dimensional analysis method

Answer 1

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Answer 2

Answer:

The equation is correct.

Explanation:

Given that,

The equation is

$\dfrac{1}{2}mv^2=mgh$

Taking left hand side

Kinetic energy $K.E=\dfrac{1}{2}mv^2$

Here, $\dfrac{1}{2}$ is constant

m = mass

v = velocity

Dimension formula of kinetic energy

$\dfrac{1}{2}mv^2=[M][L^2T^{-2}]$

Taking right hand side

Dimension formula of potential energy

Potential energy P.E = mgh

Here, g = acceleration due to gravity

h = height

m = mass

$mgh=[M][LT^{-2}][L]$

$mgh=[M][L^2T^{-2}]$

The Left hand side equal to right hand side.

Hence, The equation is correct.