Physics And Measurement Question 201
Question: The position of a particle at time $ t $ is given by the relation $ x(t)=(\frac{v _{0}^{{}}}{\alpha })(1-c _{{}}^{-\alpha t}) $ where $ v _{0}^{{}} $ ls a constant and a > 0. The dimensions of $ v _{0}^{{}} $ and $ \alpha $ are respectively
Options:
A) $ M _{{}}^{0}L _{{}}^{1}T _{{}}^{-1}andT _{{}}^{-1} $
B) $ M _{{}}^{0}L _{{}}^{1}T _{{}}^{0}andT _{{}}^{-1} $
C) $ M _{{}}^{0}L _{{}}^{1}T _{{}}^{-1}andLT _{{}}^{-2} $
D) $ M _{{}}^{0}L _{{}}^{1}T _{{}}^{-1}andLT _{{}}^{{}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Dimension of $ \alpha t=[M^{0}L^{0}T^{0}]\therefore [\alpha ]=[{{T}^{-1}}] $ .
Again $ [ \frac{v _{0}}{a} ]=[L] $ so $ [v _{0}]=[L{{T}^{-1}}] $
