Question

Let us consider an equation 1/2mv2=mgh where m is mass , v is velocity, g is acceleration due to gravity and h is height . Check weather this equation is dimentionally correct .

Answer 1

Answer:

As the equation given in question,

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

$L.H.S\ =\ \dfrac{1}{2}mv^2$

Dimensional formula of LHS can be given by

$\dfrac{1}{2}[M][LT^{-1}]^2$

$=\ \dfrac{1}{2}[ML^2T^{-2}]$

Since, $\dfrac{1}{2}$ is a constant and is dimensional less so the dimension of LHS will be $[ML^2T^{-2}]$.

R.H.S = mgh

Dimensional formula of RHS can be given by

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

$=[ML^2T^{-2}]$

As we can see the dimensional formula of LHS and RHS are the same so the given equation is dimensionally correct.

Answer 2

Answer:

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