Question

Dimensional formula of escape velocity

Answer 1

The formula for escape velocity comprises of a constant, G, which we refer to as the universal gravitational constant. The value of it is = 6.673 × 10-11 N . m2 / kg2. The unit for escape velocity is meters per second (m/s).

Dimensional Formula of Escape velocity (Ve) = L¹T¯¹

Answer 2

Answer:

Dimensional formula of Escape Velocity is - $M^0L^1T^-1$

Explanation:

Since formula of Escape velocity (VE) is $\sqrt2GM/r$

were, G = Universal gravitational constant

          M = Mass of the body.

          r = distance from the center of the mass.

Here,

The dimensional formula of the Universal Gravitational Constant is $M^{-1}L^3 T^{-2}$

The dimensional formula of earth mass is $M^1L^0T^0$

and

The dimensional formula of distance or radius of the earth is $M^0L^1T^0$.

Hence putting all these values in the above formula

=> VE = $\sqrt{[M^{-1}L^3T^{-2}][M^1L^0T^0 ]/[M^0L^1T^0 ] }$

=> VE = $\sqrt{[M^{-1+1}L^{3+0} T^{-2+0}]/[M^0L^1T^0]}$

=> VE = $\sqrt{M^{0-0}L^{3-1}T^{-2-0}}$

By simplifying the calculation we get,

       VE = $\sqrt{[M^0L^2T^{-2} }]$

Taking the square root,

we get,  VE = $\sqrt{M^0L^{1}T^{-1} }$

Hence, the dimensional formula of Escape Velocity (VE) is $\sqrt{M^0L^1T^-1 }$

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