Laws Of Motion Question 402
Question: A particle is projected on a rough horizontal ground along positive x-axis from x = 0, with an initial speed of $ {{r} _{r}} $ The friction coefficient to the ground varies with x asHere K is a positive constant. The particle comes to rest at x equal
Options:
A) $ \frac{{{r} _{r}}}{\sqrt{r}} $
B) $ \frac{r{{r} _{r}}}{Kg} $
C) $ \frac{{{r} _{r}}}{\sqrt{2Kg}} $
D) $ \frac{r{{r} _{r}}}{\sqrt{Kg}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Retardation, $ a=-\mu g=-Kx.g $
or$ V.( \frac{dV}{dx} )=-Kxg $
or$ VdV=-Kgx.Dx $
or $ \int _{v _{0}}^{0}{VdV}=-Kg\int _{0}^{x}{xdx} $
or $ x=\frac{V _{0}}{\sqrt{Kg}} $
