First slide

Physical quantities and units

Question

The acceleration due to gravity is 10 ms^-2. If the units of length and time are changed to kilometer and hour respectively, the numerical value of the acceleration due to gravity is

Moderate

A

$\frac{1}{1296}$
B

72000
C

36000
D

129600

Solution

$\begin{array}{l} n_{2} = n_{1} {[\frac{L_{1}}{L_{2}}]}^{1} {[\frac{T_{1}}{T_{2}}]}^{- 2} = 10 {[\frac{meter}{km}]}^{1} {[\frac{\sec}{hr}]}^{- 2} \\ n_{2} = 10 {[\frac{m}{10^{3} m}]}^{1} {[\frac{\sec}{3600 \sec}]}^{- 2} = 129600 \end{array}$

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