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Question

In a new system, unit of mass is 10kg, unit of length is 5m and unit of time is 10s. Then, in the new system 20 g/cc is equal to :


A
2.5×102 new units
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B
2.5×103 new units
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C
2.5×104 new units
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D
2.5×105 new units
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Solution

The correct option is C $$2.5$$$$\times10^{5}$$ new units
$$\rho _{1}=20\dfrac{gm}{cm^{3}} = M^{1}L^{-3}$$

$$\displaystyle \rho _{2}=N\dfrac{10KG}{(5)^{3}}=\dfrac{10\times 10^{3}gm}{(5\times 10^{-2})^{3}cm^{3}}$$

Equating both we get the value of $$N$$ as

$$\displaystyle N=\dfrac{20}{\dfrac{10\times 10^{3}}{(5\times 10^{-2})^{3}}}$$

       $$=2\times 10^{3}\times 5^{3}$$

       $$=250\times 10^{3}$$
       $$=2.5\times 10^{5}$$ new units.

Physics

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