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If the unit of mass, length and time be each doubled, then how the unit of power will change.

If the unit of mass, length and time be each doubled, then the unit of power remain the same.

Explanation —

The dimension of power is $\left[M L^{2} T ^{-3}\right.$ ]

$\therefore \frac{ U _{2}}{ U _{1}}$ $=\left[\frac{ M _{2}}{ M _{1}}\right]\left[\frac{ L _{2}}{ L _{1}}\right]^{2}\left[\frac{ T _{2}}{ T _{1}}\right]^{-3}=\left[\frac{2 M _{1}}{ M _{1}}\right]\left[\frac{2 L _{1}}{ L _{1}}\right]^{2}\left[\frac{2 T _{1}}{ T _{1}}\right]^{-3}$

$=2 \times 2^{2} \times 2^{-3}=1 \quad \therefore U _{2}= U _{1}$

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