Chapter 5, Problem 1MCQ

To determine

Units of work.

Answer to Problem 1MCQ

Option (d).

Explanation of Solution

Units of work can be identified using the dimensional formula. If the dimensional formula of given unit matches with the dimension formula of work, unit is correct.

Write the dimension formula of work.

    $\left[W\right]={\text{M}}^1{\text{L}}^2{\text{T}}^{-2}$

Here, $\text{M}$ is the mass, $\text{L}$ is the length and $\text{T}$ is the time.

Conclusion:

Options (a), (b) and (c) are correct. Thus, option (d) is correct.

Write the dimensional formula of $\text{N}\cdot \text{m}$.

    $\begin{array}{c}\left[\text{N}\cdot \text{m}\right]\text{=}\left({\text{M}}^1{\text{L}}^1{\text{T}}^{-2}\right)\left(\text{L}\right)\\ {\text{=M}}^1{\text{L}}^2{\text{T}}^{-2}\end{array}$

$\text{N}\cdot \text{m}$ can be used as unit of work. Thus, option (a) is correct.

Write the dimensional formula of $\text{kg}\cdot {\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}$.

    $\left[\text{kg}\cdot {\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}\right]{\text{=M}}^1{\text{L}}^2{\text{T}}^{-2}$

So, $\text{kg}\cdot {\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}$ can be used as the unit of work. Thus, option (b) is correct.

Joule is the SI unit of work. Thus, option (c) is correct.