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Question

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 :


A
3.6×104 new units
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B
6×107 new units
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C
1011 new units
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D
1.67×104 new units
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Solution

The correct option is A $$3.6\times10^{-4}$$ new units
Units of Joule are $$ML^2T^{-2}=kgm^2s^{-2}$$

$$\displaystyle n_2=n_1 \left [\frac {M_1}{M_2} \right ]\left [\frac {L_1}{L_2}\right ]^2\left [\frac {T_1}{T_2}\right ]^{-2}$$

      $$\displaystyle =1\left [\frac {1kg}{10kg}\right ]\left [\frac {1m}{1km}\right ]^2\left [\frac {1s}{1min}\right ]^{-2} $$
      
      $$\displaystyle = 1\left [\frac {1}{10}\right ]\left [\frac {1}{1000}\right ]^2\left [\frac {1}{60}\right ]^{-2} = 3.6\times 10^{-4} units$$

Physics

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