| A particle is projected on a rough horizontal ground along positive x-axis from x = 0, with an initial speed of \[{{\text{V}}_{\text{0}}}\] The friction coefficient to the ground varies with x as Here K is a positive constant. The particle comes to rest at x equal |
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A) \[\frac{{{\text{v}}_{\text{0}}}}{\sqrt{\text{Kg}}}\]
B) \[\frac{\text{2}{{\text{v}}_{\text{0}}}}{Kg}\]
C) \[\frac{{{\text{v}}_{\text{0}}}}{\sqrt{2Kg}}\]
D) \[\frac{\text{2}{{\text{v}}_{\text{0}}}}{\sqrt{Kg}}\]
Correct Answer: A
Solution :
| Retardation, |
| \[a=-\mu g=-Kx.g\] |
| or \[V.\left( \frac{dV}{dx} \right)=-Kxg\] |
| or \[V\,dV=-\,Kgx.\,Dx\] |
| or \[\int_{{{v}_{0}}}^{0}{V\,dV}=-\,Kg\,\int_{0}^{x}{x\,\,dx}\,\] |
| or \[x=\frac{{{V}_{0}}}{\sqrt{Kg}}\] |
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