Question

The dimension of impulse is $\left[ ML{ T }^{ -1 } \right]$. Find \left[ ML{ T }^{ -1 } \right] +\left[ ML{ T }^{ -1 } \right] =\\_ \\_ \\_ \\_ \\_
$A. \left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ 0 } \right]$
$B. \left[ ML{ T }^{ -1 } \right]$
$C. 2\left[ ML{ T }^{ -1 } \right]$
$D. None \ of \ these$

Answer 1

To solve this question, use the basic concept of dimension analysis. According to dimension analysis, we can add or subtract only those quantities that have the same dimensions and their result after addition or subtraction will also be the same. The dimensional equation on both sides should be the same. Use this information to find the result of addition of these two dimensional quantities.

Complete solution:
According to the principle of homogeneity, the dimensions of each of the terms of a dimensional equation on both sides should be the same. On left-hand side both the terms have the same dimensions i.e. $\left[ ML{ T }^{ -1 } \right]$. So, the term on the right-hand side will also have the same quantity.
Thus, we can write,
$\left[ ML{ T }^{ -1 } \right] +\left[ ML{ T }^{ -1 } \right] =\left[ ML{ T }^{ -1 } \right]$

So, the correct answer is option B i.e. $\left[ ML{ T }^{ -1 } \right]$.

Note:
Students must keep in mind that that dimensional analysis cannot help them to determine any dimensionless constants in the equation. An equation can be dimensionally homogeneous but invalid if the equation is not fully-balanced. With the help of dimension analysis, we can check the correctness of the physical equation and also derive the physical quantities involved in a physical phenomenon.