Physics And Measurement Question 188
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).
Options:
A) The relation is dimensionally correct
B) The relation is dimensionally incorrect
C) The relation may be dimensionally correct
D) None of the above
Show Answer
Answer:
Correct Answer: A
Solution:
[a] LHS= $ [x _{1}+x _{2}]=[x _{1}]=[x _{2}]=[M^{0}LT^{0}] $ RHS= $ [ \frac{a _{1}a _{2}t^{2}}{2(a _{1}+2a)} ]=\frac{[L{{T}^{-2}}][L{{T}^{-2}}][T^{2}]}{[L{{T}^{-2}}]}=[M^{0}LT^{0}] $
$ \because $ LHS=RHS According to homogeneity principle, equation is dimensionally correct.
Hence, option [a] is correct.
