In a new system of unit mass is measured in multiple of x kg, length in multiple of y m and time in multiple of z second. What is the value of 10 J in new system of unit?

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$\frac{10 {xy}^{2}}{z^{2}}$

$\frac{10 z^{2}}{{xy}^{2}}$

$\frac{10 x^{2} y}{z^{2}}$

$\frac{{xy}^{2}}{10 z^{2}}$

answer is D.

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Detailed Solution

$M = xKg \Rightarrow kg = \frac{M}{x}, L = ym \Rightarrow m = \frac{L}{Y}, T = Zsec \Rightarrow \sec \frac{T}{Z}$
$\begin{array}{l} 10 J = 10 {kgm}^{2} s^{- 2} = 10 \frac{M}{x} \cdot \frac{T^{- 2}}{Z^{- 2}} \\ = \frac{10 Z^{2}}{{xy}^{2}} new unit \end{array}$

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