Question

consider an equation 1/2mv^2 = mgh where m is the mass of the body , v its velocity ,g is the acceleration due to gravity and h is the height. check whether this equation is dimensionally correct.

Answer 1

$\huge\textbf{ANSWER}$

$\frac{1}{2} m {v}^{2} = mgh$
$<b>$
Let's check by LHS and RHS method

So LHS

Dimensional formula of 1/2mv² = [M¹ L²T-²]

so now RHS = mgh

Dimensional formula of mass = [M¹]

dimensional formula of g (acceleration due to gravity) = [ L¹ T-²]

Dimensional formula of height(length) is [L¹]

so dimensional formula of mgh will be

= [M¹ L²T-² ]

so LHS = RHS

So the given formula is dimensionally correct.

Thanks

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Answer 2

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