Answer
The correct answer is (b) $kg\cdot m^2 \cdot s^{-2}\cdot K^{-1}$
Work Step by Step
$v = \sqrt{\gamma ~k_B ~T / m}$
Let $x$ be the units of $k_B$
$m/s = \sqrt{(x)(K)/kg}$
$m^2/s^2 = (x)(K)/kg$
$x = \frac{kg\cdot m^2}{s^2\cdot K} = kg\cdot m^2 \cdot s^{-2}\cdot K^{-1}$
The correct answer is (b) $kg\cdot m^2 \cdot s^{-2}\cdot K^{-1}$
