Question

let us consider an equation 1/2mv^=mgp where m is the mass of the body v it's velocity g is acceleration due to gravity and h is the height check weather this equatio
n is dimensionally correct​

Answer 1

Correct Question:

Let us consider an equation ½mv² = mgh where m is the mass of the body, v it's velocity, g is acceleration due to gravity and h is the height. Check weather equation is dimensionally correct.

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Solution:

L.H.S. = ½mv²

Here, m is mass measured in kg and velocity is measured in m/s, therefore v² = m²/s² and ½ is numerical constant hence, it's dimension will be zero.

L.H.S. = kg m²/s²

L.H.S. = $\sf{[M \ L^{2} \ T^{-2}]}$...(1)

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R.H.S. = mgh

Here, m is mass measured in kg and g is acceleration due to gravity measured in m/s² and h is height measured in m.

R.H.S. = kg (m/s²) m

R.H.S. = kg m²/s²

R.H.S. = $\sf{[M \ L^{2} \ T^{-2}]}$...(2)

From (1) and (2), we get

L.H.S. = R.H.S.

Hence, the equation ½mv² = mgh is dimensionally correct.

Answer 2

Answer:

Since, potential energy and Kinetic energy are the form of energies.

Their dimensional formula will be [M L² T^-2 ]