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# If the unit of work is $100J$, the unit of power is $1KW$, the unit of time in second is:A) ${10^{ - 1}}$B) ${10^{}}$C) ${10^{ - 2}}$D) ${10^{ - 3}}$

Last updated date: 06th Sep 2024
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Hint: As we know that, we have to find the unit of time. According to the question we have energy (unit of work) and power. So as per given data we can use the following formula to find the unit of time. It can also be solved using dimensional formulas.

The data given in the question are
Energy = $100J$
Power = $10KW$ = $1000W$
We have to find the unit of time in second,
${{Energy }} = {{ Power }} \times {{ Time}}$
${{Time = }}\dfrac{{{{Energy}}}}{{{{Power}}}} = \dfrac{{100}}{{1000}} = \dfrac{1}{{10}} = {10^{ - 1}}$.

Energy: is the capacity when we can do the work. The unit of energy is joule.
Power: it is the rate of doing the work. The unit of power is watt.
Work: the amount of energy transfer that occurs when a particle is moved to some distance by an external force. The unit of work is also joule.
We can also solve the question using dimension formulas as shown below.
Energy = $100J$ $= \left[ {{{M }}{{{L}}^2}{{ }}{{{T}}^{ - 2}}} \right]$
Power = $10KW$ = $1000W$ = $= \left[ {{{M }}{{{L}}^2}{{ }}{{{T}}^{ - 3}}} \right]$
${{Time = }}\dfrac{{{{Energy}}}}{{{{Power}}}} = \dfrac{{100}}{{1000}} = \dfrac{{{{M}}{{{L}}^2}{{{T}}^{ - 2}}}}{{{{M}}{{{L}}^2}{{{T}}^{ - 3}}}} = {{{T}}^1} = \dfrac{1}{{10}} = {10^{ - 1}}$.

Note: The base formula used here is Energy = Power × Time.
If data of the time and power is given in the question then we can find energy by multiplying both power and time. Similarly, if we have the data of time and energy then we can find the power by dividing both time and energy. If we have the data of power and energy then we can get the value of time by dividing both power and energy.
The dimension formula for some physical quantities:
Force $= {{mass }} \times {{ acceleration = }}\left[ {{M}} \right] \times \left[ {{{L }}{{{T}}^{ - 2}}} \right] = \left[ {{{M L }}{{{T}}^{ - 2}}} \right]$
Work $= {{force }} \times {{ distance = }}\left[ {{{M L }}{{{T}}^{ - 2}}} \right] \times \left[ {{L}} \right] = \left[ {{{M }}{{{L}}^2}{{ }}{{{T}}^{ - 2}}} \right]$
Energy = work $= \left[ {{{M }}{{{L}}^2}{{ }}{{{T}}^{ - 2}}} \right]$
Power $= \dfrac{{{{work}}}}{{{{time}}}} = \dfrac{{\left[ {{{M }}{{{L}}^2}{{ }}{{{T}}^{ - 2}}} \right]}}{{\left[ {{T}} \right]}} = \left[ {{{M }}{{{L}}^2}{{ }}{{{T}}^{ - 3}}} \right]$.