Question

A student writes the escape velocity as:
$V_{e}=\sqrt{\frac{G M}{R^{2}}}$
The equation is:

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

Answer 1

Answer: (A)

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

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

Hence; equation is dimensionally incorrect

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

Hence; given equation is dimensionally incorrect