Physics And Measurement Question 202
Question: A body travels uniformly a distance of $ (S+\Delta S) $ in a time $ (t\pm \Delta t) $ . What may be the condition so that body within the error limits move with a velocity $ (\frac{S}{t}\pm \frac{\Delta S}{\Delta t}) $ ?
Options:
A) $ \frac{\Delta t}{t}+\frac{S(\Delta t) _{{}}^{2}}{(\Delta S)t _{{}}^{2}}=\pm 1 $
B) $ \frac{\Delta t}{t}+\frac{S\Delta t _{{}}^{{}}}{\Delta St _{{}}^{{}}}=\pm 1 $
C) $ \frac{\Delta t}{t}+\frac{(\Delta S)t _{{}}^{{}}}{S(\Delta t) _{{}}^{{}}}=\pm 1 $
D) $ \frac{\Delta t}{t}+\frac{S _{{}}^{2}\Delta t _{{}}^{{}}}{(\Delta S) _{{}}^{2}t _{{}}^{{}}}=\pm 1 $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ V=\frac{S}{t} $
$ \Delta V=\frac{1}{t}.\frac{\partial s}{\partial s}.\Delta S+\frac{S}{t^{2}}\Delta t=( \frac{\Delta S}{t}+\frac{S\Delta t}{t^{2}} ) $ So $ \frac{\Delta S}{t}+\frac{S\Delta t}{t^{2}}=\frac{\Delta S}{\Delta t}.\frac{\Delta t}{t}+\frac{(\Delta S).S(\Delta t^{2})}{(\Delta S).t^{2}(\Delta t)} $
Or $ \frac{\Delta S}{\Delta t}[ \frac{\Delta t}{t}+\frac{S{{(\Delta t)}^{2}}}{(\Delta S)t^{2}} ]=\pm \frac{\Delta S}{\Delta t} $ (given)
So, $ \frac{\Delta t}{t}+\frac{S{{(\Delta t)}^{2}}}{(\Delta S)t^{2}}=\pm 1 $
