Question

Which of the following is not represented in correct unit
(A) $ \dfrac{{Stress}}{{Strain}} = N/m^2$
(B) Surface tension $=N/m$
(C) Energy $=kg-m/sec$
(D) Pressure $=N/m$

Answer 1

Hint: The unit of each and every formula is determined by simply writing the units of the basic constituents of the formula together. For example, Force is mass times acceleration thus the unit of force is newton which becomes $ kg{m \mathord{\left/
 {\vphantom {m {{{\sec }^2}}}} \right.} {{{\sec }^2}}} $ where $ kg $ is the SI unit of mass and $ {m \mathord{\left/
 {\vphantom {m {{{\sec }^2}}}} \right.} {{{\sec }^2}}} $ is the unit of acceleration.
So, for this question we need to find out the unit of each and every given option and check it with the units given with them to find out whether the option is correct or not.

Complete Step By Step Answer:
Stress is force per unit area that arises when a material is subjected to an external pressure.
The unit of stress $ = \dfrac{{Force}}{{Area}} = \dfrac{N}{{{m^2}}} $
Strain is the measure of how much the object has deformed with respect to its original length.
The unit of stress $ = \dfrac{{deformation}}{{length}} = \dfrac{{\Delta l}}{l} = \dfrac{m}{m} $ which is dimensionless.
Thus, the unit of $ \dfrac{{Stress}}{{Strain}} = {N \mathord{\left/
 {\vphantom {N {{m^2}}}} \right.} {{m^2}}} $ as the denominator is dimensionless.
Surface tension is the tendency of the surface of a liquid that allows it to resist an external force.
The unit of surface tension $ = \dfrac{{Force}}{{length}} = {N \mathord{\left/
 {\vphantom {N m}} \right.} m} $
Energy is the ability to do work thus the unit of energy is the same as that of work. And work is done when an external force is applied on an object over a displacement.
The unit of work = the unit of energy $ = Force \times displacement = N \times m $
Pressure is also defined as the force exerted per unit area.
The unit of pressure $ = \dfrac{{Force}}{{Area}} = \dfrac{N}{{{m^2}}} $
Thus, from all the above derivations we can see the unit of energy is given incorrectly.
The correct option is (C).

Note:
From the above solution we can see that each unit of the given complex function is made by using the units of the simpler. Thus, these simpler units play a vital role in analysing the dimension of a given complex unit. Sometimes even two different units will have the same dimension as in case of option (A) and (D) which is completely normal in physics. The only place of making any kind of mistake is when we apply the wrong basic units in order to find the unit of a complex formula.