A particle moves in a straight line with retardation proportional to its displacement. Its loss of k

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5.Work, Energy, Power and Collision

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A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:

A

$x^2$

B

$e^x$

C

$x$

D

$log_e\,x$

Solution

According to question $:$

$\frac{\mathrm{d} \mathrm{v}}{\mathrm{dt}} \propto \mathrm{x}$

or $\quad \frac{d v}{d x} \cdot \frac{d x}{d t} \propto x$

or $\quad \frac{d v}{d x} \cdot v \propto x$

$\mathbf{o r}$ $vdv$ $\propto$ $xd$ $x$

$\therefore$ $\mathrm{V}^{2} \text { oc } \mathrm{X}^{2}$

Standard 11

Physics

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