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)

$LHS=[x_1+x_2]=[x_1]=[x_2]=[M^{o}L{T}^o]$
$RHS=[\frac{a_1{a}_2{t}^2}{2(a_1+a_2)}]=\frac{[L{T}^{-2}][L{T}^{-2}][T^2]}{[L{T}^{-2}]}=[M^{0}L{T}^0]$
$\because LHS=RHS$
According to homogeneity principle, equation is dimensionally correct.
Hence, option $(1)$ is correct.