Question

If the acceleration due to gravity is $10\, ms^{-2}$ and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is

• A. $360000$
• B. $72,000$
• C. $36,000$
• D. $129600$

Answer 1

Answer: (D)

$n_{2} = n_{1}\left[\frac{L_{1}}{L_{2}}\right]^{1}\left[\frac{T_{1}}{T_{2}}\right]^{-2}$
$=10\left[\frac{meter}{km}\right]^{1}\left[\frac{s}{hr}\right]^{-2}$
$n_{2}=10\left[\frac{m}{10^{3}m}\right]^{1}\left[\frac{s}{3600s}\right]^{-2}$
$=129600$