Question

Check whether equation 1/2mv² = mgh is dimensionally correct?​

Answer 1

$\sf{Required\: answer:-}$

We can say that 1/2 mv² = mgh Dimensionally correct .

➺Given to check whether the equation dimensionally correct :-

1/2 mv² = mgh

➺ EXPLANATION :-

1/2 mv² = mgh

⟹Take L.H.S

1/2 mv²

As 1/2 is contsant we shall neglect it.

⟹Take mv²

Writing dimensional formula for mv²

mv² where,

• m = mass
• v = velocity

We know that ,

⟹m= [M]

⟹v = m/s [metre/second]

⟹ v = [M⁰ L¹ T ⁻¹]

⟹mv² = [M] [M⁰ L¹ T ⁻¹]²

⟹mv² = [M¹ ][L²T ⁻²]

⟹L.H.S = [M¹ L² T ⁻²]

___________________

Take R.H.S

mgh

where,

• m = mass
• g = gravity
• h = height

Writing dimensional formula

⟹m = [M]

g = m/s² [metre/second²]

⟹g = [M⁰ L ¹T⁻²]

⟹h = height nothing but unit is metre

⟹h = [L]

⟹mgh = [M] [M⁰ L ¹T⁻²] [L]

⟹mgh = [M¹ L² T⁻²]

⟹R.H.S = [M¹ L² T⁻²]

So,

L.H.S = R.H.S = [M¹ L² T⁻²]

Since, we can say that 1/2 mv² = mgh Dimensionally correct .

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Extra information:-

For writing the Dimensional formula we use this

[M L T ] here,

• M = mass
• L = length (metres)
• T = time (seconds)

and We can write the dimensional formula easily If we know the units of the particular quantity.