Question

Veify dimensionaly Potential energy = m²g¹h² is correct or wrong ,where m is mass,g is gravity, & h is height.​

Answer 1

DIMENSIONS OF POTENTIAL ENERGY = M¹L²/T²...........A

DIMENSIONS OF GIVEN EXPRESSION = M²(L/T²)L²

= M²L³/T².........S

BY COMPARING A AND S

THE GIVEN EXPRESSION FOR POTENTIAL ENERGY IS INCORRECT

Answer 2

Answer:-

The Above Given Expression that Potential energy = m²g¹h² is wrong.

Explanation:-

We know that Potential Energy is a type of energy so its dimensional formula will be $\bf [ML^2T^{-2}]$

So if the above formula is correct then,

$\\ \longrightarrow\textbf{D of P.E. = D of \tt m^2g^1h^{-2} }.$

So Now,

We know that,

• Dimension of mass = [M].

• Dimension of g = $\tt [LT^{-2}].$

• Dimension of h = [L]

(We Know that g is gravitational acceleration)

$\\ \bf{\overbrace{\textbf{D of acceleration = D of g.}}^{\textbf{ \underline{ \red{Dimension formula of g}}}}} \\ \\ \tt\mapsto A = \dfrac{v-u}{t} = \dfrac{\frac{Displacement}{time}}{time}.\:\:\:\:\:\: \\ \\ \bf\mapsto D \: \: of \: \: A = [\dfrac{L}{T \times T}] = [LT^{-2}].$

Where,

• D is Dimension.

• v is final Velocity.

• u is initial velocity.

• t is time.

Therefore,

$\\ \texttt{ \mapsto D of \tt m^2g^1h^{-2} } =\tt [M]^2\times[LT^{-2}]\times[L^2].$

$\\ \tt = [M^{2}L^{1+2}T^{-2}].$

$\\ \bf = [M^2L^3T^{-2}] \neq [ML^2T^{-2}].$

Clearly Dimension Of Potential Energy Is Not Equal To Dimension Of m²g¹h².

Therefore The Above Expression Is wrong.