SATHEE: Laws Of Motion Question 402

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 $Math input error$ 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) $Math input error$

B) $Math input error$

C) $Math input error$

D) $Math input error$

Show Answer

Answer:

Correct Answer: A

Solution:

Retardation, $a = - μ g = - K x . g$

or $V . (\frac{d V}{d x}) = - K x g$

or $V d V = - K g x . D x$

or $\int_{v_{0}}^{0} V d V = - K g \int_{0}^{x} x d x$

or $x = \frac{V_{0}}{\sqrt{K g}}$

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Laws Of Motion Question 402

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