Question

Find the physical quantity.
\[(A)ML{T^{ - 1}}\]
\[(B)M{L^0}{T^{ - 2}}\]

Answer 1

Hint: The checking relations between the physical quantities by identifying the dimensions of these physical quantities are called dimensional analysis. All the physical quantities can be expressed using 7 basic dimensions. These are mass\[\left( M \right)\], length\[\left( L \right)\], time\[\left( t \right)\], current\[\left( A \right)\], temperature\[\left( K \right)\], luminous intensity\[\left( {Cd} \right)\], and amount of substance\[\left( {mol} \right)\].

Formula used:
\[Momentum = Force \times time\]
\[Surface\]\[tension = \dfrac{{force}}{{unitlength}}\]

Complete step-by-step solution:
Momentum is simply called as the mass in motion. If the object is moving it possesses momentum, because all the objects have mass. The product of its mass and the velocity by which the object is moving is called the Momentum of a body.
\[\begin{gathered}
  Momentum = Force \times time \\
  Force = mass \times acceleration \\
  momentum = mass \times acceleration \times time \\
\end{gathered} \]
The dimensional formula of these basic quantities
The dimensional formula of mass is\[\left[ M \right]\].
The dimensional formula of acceleration is\[\left[ {L{T^{ - 2}}} \right]\].
The dimensional formula of time is\[\left[ T \right]\].
Substituting these dimensional formulas
\[I = Mass \times acceleration \times time\]
\[ \Rightarrow \left[ I \right] = \left[ M \right] \times \left[ {L{T^{ - 2}}} \right] \times \left[ T \right]\]
\[ \Rightarrow \left[ I \right] = \left[ {ML{T^{ - 1}}} \right]\]
Hence, the Impulse is dimensionally represented as \[\left[ {ML{T^{ - 1}}} \right]\]
Surface tension is defined as the tendency of the fluid surfaces to shrink into the minimum surface area possible. It can be determined by the difference in the interactions between the molecules of the fluid with the molecules of the flask or beaker or the molecules of the storage wall. \[Surface{\text{ }}tension = \dfrac{{force}}{{unitlength}}\]
\[Surface{\text{ }}tension = \dfrac{{{M^1}{L^1}{T^{ - 2}}}}{{{L^1}}} = M{L^0}{T^{ - 2}}\]
Hence, the surface tension is dimensionally represented as \[M{L^0}{T^{ - 2}}\]
Some examples of the surface tension are, the needle is floating on the surface of the water, the water droplets on the surface of the leaf look like small bubbles for some time, and the raindrop is circular due to surface tension.

Note: A physical quantity's dimension is more fundamental than some unit of scale used to express the quantity of that physical amount. Major uses of dimensional equations- to test a physical equation's correctness, to derive the relation between a physical phenomenon involving different physical quantities. Move from one control configuration to another.