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PhysicsW.E.P.MiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

Two particles of masses $m_{1}$ and $m_{2}$ are initially at rest at an infinite distance apart. If they approach each other under their mutual interaction given by $F = - \frac{K}{r^{2}}$ . Their speed of approach at the instant when they are at a distance $d$ apart is

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Answer:

Solution:

Let $μ$ be the reduced mass of the system and $v$ be the approach speed of the particles, then

$\frac{1}{2} {μv}^{2} = \int_{\infty}^{d} \vec{F} . d \vec{r}$

$\Rightarrow \frac{1}{2} \frac{m_{1} m_{2}}{m_{1} + m_{2}} v^{2} = - \int_{\infty}^{d} \frac{K}{r^{2}} dr$

$∴ v = \sqrt{\frac{2 K}{d} [\frac{1}{m_{1}} + \frac{1}{m_{2}}]}$

Subject:PhysicsTopic:W.E.P.Subtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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