A particle of mass m moves on positive x-axis under the influence of force acting towards the origin given by -kx2i^. If the particle starts from rest at x=a, the speed it will attain when it crosses the origin is

a=Fm=-kx2m∴ v·dvdx=-kx2mor∫0vvdv=∫a0-kx2mdxv22=ka33mv=2ka33m

A particle of mass m moves on positive x-axis under the influence of force acting towards the origin given by -kx2i^. If the particle starts from rest at x=a, the speed it will attain when it crosses the origin is

a=Fm=-kx2m∴ v·dvdx=-kx2mor∫0vvdv=∫a0-kx2mdxv22=ka33mv=2ka33m

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A particle of mass $m$ moves on positive $x$ -axis under the influence of force acting towards the origin given by $- k x^{2} \hat{i}$ . If the particle starts from rest at $x = a$ , the speed it will attain when it crosses the origin is

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$\sqrt{\frac{m a}{2 k}}$

$\sqrt{\frac{k}{m a}}$

$\sqrt{\frac{2 k}{m a}}$

None of these

answer is D.

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Detailed Solution

$a = \frac{F}{m} = \frac{- k x^{2}}{m}$
$∴ v \cdot \frac{d v}{d x} = - \frac{k x^{2}}{m}$
or

$\int_{0}^{v} v d v = \int_{a}^{0} - \frac{k x^{2}}{m} d x$
$\frac{v^{2}}{2} = \frac{k a^{3}}{3 m}$
$v = \sqrt{\frac{2 k a^{3}}{3 m}}$

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A particle of mass m moves on positive x-axis under the influence of force acting towards the origin given by -kx2i^. If the particle starts from rest at x=a, the speed it will attain when it crosses the origin is

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A particle of mass $m$ moves on positive $x$ -axis under the influence of force acting towards the origin given by $- k x^{2} \hat{i}$ . If the particle starts from rest at $x = a$ , the speed it will attain when it crosses the origin is