In a new system of units, unit of mass is 10 kg, unit of length is 1 km and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is

Options

A. `3.6 xx 10^(-4)` new units
B. `6 xx 10^(7)` new units
C. `10^(11)` new units
D. `1.67 xx 10^(4)` new units

Answer

A

Explanation

The dimensional formula of energy is `[ML^(2)T^(-2)]`
`n_(2)= 1[(1kg)/(10kg)]^(1)[(1m)/(1km)]^(2)[(1s)/(1min)]^(-2)`
`= (1)/(10) xx (1)/(10^(6)) xx (1)/(60)^(-2)= (3600)/(10^(7))= 3. 6 xx 10^(-4)`