Question

Using principle of Homogencity of equation, check whether the equation is correct T=2¶√g/l

Answer 1

$\underline{\underline{\sf\bf\bigstar\huge ANSWER \bigstar}}$

Equation ,

    $\sf T=2\pi\sqrt{\dfrac{l}{g}}$

Here ,

     T = Time

      l = Length

      g = Gravity

_____________________________________

$\longrightarrow \sf [M^0L^0T^1]=\sqrt{\dfrac{[M^0L^1T^0]}{[M^0L^1T^-2]}} \\\\\longrightarrow [M^0L^0T^1]=\sqrt{[M^0L^0T^2]} \\\\\longrightarrow [M^0L^0T^1]=[M^0L^0T^2]^\frac{1}{2} \\\\\longrightarrow [M^0L^0T^1]=[M^0L^0T^1]$

∴ The equation is dimensionally correct