Question

Choose the quantity which has the unit \[kg{{m}^{2}}{{s}^{-2}}\].
A. kinetic energy only
B. work done only
C. potential energy only
D. all the above

Answer 1

Hint: Recall the basic definition of each quantity given in the option i.e., kinetic energy, work done and potential energy, thereafter find the units for each quantity and compare them.

Complete step by step answer:

As we know that the formula for kinetic energy \[\left( K \right)\], work done \[\left( W \right)\] and potential energy \[\left( P \right)\] is given by,
\[K=\dfrac{1}{2}m{{v}^{2}}\]
\[W=F.d\]
\[P=mgh\]
Where,
\[\begin{align}
  & K\text{ = kinetic energy of the body} \\
 & m\text{ = mass of the body} \\
 & v\text{ = velocity of the body} \\
 & W\text{ = work done} \\
 & F\text{ = Force applied} \\
 & d\text{ = displacement of the body} \\
 & P\text{ = gravitational potential energy of the body} \\
 & g\text{ = acceleration due to gravity} \\
 & h\text{ = height} \\
\end{align}\]
Now on writing the units of each quantity by using the above formulae, we have
unit of kinetic energy = \[\left( kg \right).{{\left( m{{s}^{-1}} \right)}^{2}}\] = \[kg{{m}^{2}}{{s}^{-2}}\],
unit of work done = \[\left( kg.m{{s}^{-2}} \right).\left( m \right)\] = \[kg{{m}^{2}}{{s}^{-2}}\],
and unit of potential energy = \[\left( kg \right).\left( m{{s}^{-2}} \right).\left( m \right)\] = \[kg{{m}^{2}}{{s}^{-2}}\]
We observe that all the given three quantities have same units i.e., \[kg{{m}^{2}}{{s}^{-2}}\]
Hence, the correct option is D, i.e., all the above.

Additional Information:
Kinetic energy is a scalar quantity (it has magnitude but no direction). It is always a positive number, and its S.I. unit is \[kg{{m}^{2}}{{s}^{-2}}\].
Potential energy is a scalar quantity and having the same S.I. unit as of kinetic energy i.e., \[kg{{m}^{2}}{{s}^{-2}}\].
Work is also a scalar quantity and its S.I. unit is \[kg{{m}^{2}}{{s}^{-2}}\] or N-m.
The above units of these quantities are also known as ‘joule’.

Note: Students need to know the formula for kinetic energy \[\left( K \right)\], work done \[\left( W \right)\] and potential energy \[\left( P \right)\] so that they can write the units of all the physical quantities present in their mathematical expressions. In this way, students can find and compare the units of all quantities. Here students should be very careful while doing simplification after writing units of each quantity separately.