Question

$A$ bus travels distance $x_1$ when accelerates from rest at constant rate $a_{2}$ for some time and after that travels a distance $x_{2}$ when decelerates at a constant rate $a_{2}$ to come to rest. A student established a relation $x_{1} +x_{2} =\frac{a_{1}a_{2}t^{2}}{2(a_{1}+a_{2})}$
Choose the correct option(s).

• A. The relation is dimensionally correct
• B. The relation is dimensionally incorrect
• C. The relation may be dimensionally correct
• D. None of the above

Answer 1

Answer: (A)

$LHS= [x_{1} + x_{2}] = [x_{1}] = [x_{2}] = [M^{o}LT^{o}]$
$RHS =[\frac{a_{1}a_{2}t^{2}}{2(a_{1}+a_{2})}] =\frac{[LT^{-2}][LT^{-2}][T^{2}]}{[LT^{-2}]}=[M^{0}LT^{0}]$
$\because LHS=RHS$
According to homogeneity principle, equation is dimensionally correct.
Hence, option $(1)$ is correct.