Question

If we take units of mass, length and time as $2\text{kg},2\text{m}$ and $2\text{s}$ respectively then the unit of energy will be

• A. $8\text{J}$
• B. $6\text{J}$
• C. $4\text{J}$
• D. $2\text{J}$

Answer 1

The correct option is D $2\text{J}$

We know the dimensional formula of energy,
$\left[E\right]=\left[M^1{L}^2{T}^{-2}\right]$
For this, the unit of energy is $1\text{J}$.
If units of mass, length and time becomes $2\text{kg},2\text{m}$ and $2\text{s}$ respectively then the new dimension of energy will be,
$\left[E^{{}^{\prime }}\right]=\left[\right(2M{)}^1\left(2L{)}^2\right(2T{)}^{-2}]$
$\Rightarrow \left[E^{{}^{\prime }}\right]=2\left[M^1{L}^2{T}^{-2}\right]=2\left[E\right]$
For this, the unit of energy will be $2\text{J}$.