Question

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

Answer 1

We know that,

Unit formula of power

$power\left(p\right)=\frac{work}{time}$

$p=\frac{force\times displacment}{time}$

$p=force\times velocity$

Now, dimension formula of power

$=\left[ML{T}^{-2}\right]\left[L{T}^{-1}\right]$

If mass, length and time is doubled

Then,

$p=\left[ML{T}^{-2}\right]\left[L{T}^{-1}\right]$

$p=\left[M{L}^2{T}^{-3}\right]$

$p=\left[2M{\left(2L\right)}^2{\left(2T\right)}^{-3}\right]$

$p=\left[M{L}^2{T}^{-3}\right]$

Hence, the unit of power is $p=\left[M{L}^2{T}^{-3}\right]$

No change will occur in the unit.