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$$\times {10}^2$ new units
• B. $2.5$$\times {10}^3$ new units
• C. $2.5$$\times {10}^4$ new units
• D. $2.5$$\times {10}^5$ new units

Answer 1

Answer: (D)

$2.5$$\times {10}^5$ new units

${\rho }_1=20\frac{gm}{c{m}^3}=M^1{L}^{-3}$

${\rho }_2=N\frac{10KG}{(5{)}^3}=\frac{10\times {10}^{3}gm}{(5\times {10}^{-2}{)}^{3}c{m}^3}$

Equating both we get the value of $N$ as

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

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

$=250\times {10}^3$

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