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PhysicsModern PhysicsMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2 : 1$ . The ratio of their nuclear size will be

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Answer:

Solution:

According to the law of conservation of momentum, we get

$m_{1} v_{1} = m_{2} v_{2}$

Or $(\frac{m_{1}}{m_{2}}) = (\frac{v_{2}}{v_{1}})$

But $m = \frac{4}{3} π r^{3} ρ o r m \propto r^{3}$

$\Rightarrow \frac{m_{1}}{m_{2}} = \frac{r_{1}^{2}}{r_{2}^{3}}$

$∴ \frac{r_{1}^{3}}{r_{2}^{3}} = \frac{v_{2}}{v_{1}} = \frac{1}{2}$

$\Rightarrow \frac{r_{1}}{r_{2}} = {(\frac{1}{2})}^{\frac{1}{3}}$

$∴ r_{1} : r_{2} = 1 : {(2)}^{\frac{1}{3}}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Modern PhysicsSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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