First slide

Dimensions of physical quantities

Question

A bus travels distance x₁ when accelerates from rest at constant rate a₁ for some time and after that travels a distance x₂ when decelerates at a constant rate a₂ to come to $x_{1} + x_{2} = \frac{a_{1} a_{2} t^{2}}{2 (a_{1} + a_{2})} .$ Choose the correct option(s).

Moderate

A

The relation is dimensionally correct
B

The relation is dimensionally incorrect
C

The relation may be dimensionally correct
D

None of the above

Solution

$\begin{array}{l} LHS = [x_{1} + x_{2}] = [x_{1}] = [x_{2}] = [M^{0} L T^{0}] \\ \begin{aligned} RHS & = [\frac{a_{1} a_{2} t^{2}}{2 (a_{1} + a_{2})}] \\ = \frac{[L T^{- 2}] [L T^{- 2}] [T^{2}]}{[L T^{- 2}]} = [M^{0} L T^{0}] \\ ∵ LHS & = RHS \end{aligned} \end{array}$
According to homogeneity principle, equation is dimensionally
correct.
Hence, option (a) is correct.

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