Question
Download Solution PDFA force F is given by F = at + bt2 where t is time, what are the dimension of a and b.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Principle of homogeneity of dimensions:
- According to this principle, a physical equation will be dimensionally correct if the dimensions of all the terms occurring on both sides of the equation are the same.
- This principle is based on the fact that only the physical quantities of the same kind can be added, subtracted, or compared.
- Thus, velocity can be added to velocity but not to force.
EXPLANATION
Given - F = at + bt2
From the principle of dimensional homogeneity, the left-hand side of the equation dimensionally equal to the right-hand side of the equation.
The dimension formula of force (F) = [MLT-2]
∴ [MLT-2] = [a] [T]
\(⇒ \left[ a \right] = \frac{{\left[ {ML{T^{ - 2}}} \right]}}{{\left[ T \right]}} = \left[ {ML{T^{ - 3}}} \right]\)
For second term,
⇒ [MLT-2] = [b] [T2]
\(\Rightarrow \left[ b \right] = \frac{{\left[ {ML{T^{ - 2}}} \right]}}{{\left[ {{T^2}} \right]}} = \left[ {ML{T^{ - 4}}} \right]\)
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