Question

A student writes the escape velocity as:
$V_e=\sqrt{\frac{GM}{R^2}}$
The equation is:

• A. Dimensionally incorrect
• B. Dimensionally correct
• C. Numerically correct
• D. Both (a) and (c)

Answer 1

Answer: (A)

Dimensions of $RHS={\left[\frac{M^{-1}{L}^3{T}^{-2}\times M}{L^2}\right]}^{1/2}$

$={\left[M^{0}L{T}^{-2}\right]}^{1/2}=\frac{[L{]}^{1/2}}{T}\ne LHS$

Hence; equation is dimensionally incorrect

$\text{ Also; }{V}_e=\sqrt{\frac{2GM}{R}}$

Hence; given equation is dimensionally incorrect