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Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassMiscellaneousHard2 minPYQ_2023

PhysicsHardinteger

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3 : 2$ . The ratio of their nuclear sizes will be ${(\frac{x}{3})}^{\frac{1}{3}}$ . The value of ‘ $x$ ’ is:

Answer:

Solution:

Given here, $\frac{v_{1}}{v_{2}} = \frac{3}{2}$

Using conservation of momentum during disintegration, we have

$m_{1} v_{1} = m_{2} v_{2} \Rightarrow \frac{m_{1}}{m_{2}} = \frac{2}{3}$

Since, $m = \frac{4}{3} π R^{3} ρ$

We have $m \propto R^{3} (∵ nuclear mass density, ρ = constant)$

$\frac{m_{1}}{m_{2}} = {(\frac{R_{1}}{R_{2}})}^{3}$

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

So, $x = 2$ .

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2023

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