Two $α$ - particles have the ratio of their velocities as 3:2 on entering the field. If they move in different circular paths, then the ratio of the radii of their paths is :

2:3

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3:2

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9:4

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4:9

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Solution

The correct option is B 3:2
As the lorentz force which acts on the particle will acts as centripetal force
$∴ q v B = \frac{m v^{2}}{r}$
$∴ r = \frac{m v}{q B} \Rightarrow r \propto v$ or $\frac{r_{A}}{r_{B}} = \frac{v_{A}}{v_{B}} = \frac{3}{2}$

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Two α - particles have the ratio of their velocities as 3:2 on entering the field. If they move in different circular paths, then the ratio of the radii of their paths is :

The correct option is B 3:2As the lorentz force which acts on the particle will acts as centripetal force ∴qvB=mv2r∴r=mvqB⇒r∝v or rArB=vAvB=32

Two $α$ - particles have the ratio of their velocities as 3:2 on entering the field. If they move in different circular paths, then the ratio of the radii of their paths is :

The correct option is B 3:2
As the lorentz force which acts on the particle will acts as centripetal force
$∴ q v B = \frac{m v^{2}}{r}$
$∴ r = \frac{m v}{q B} \Rightarrow r \propto v$ or $\frac{r_{A}}{r_{B}} = \frac{v_{A}}{v_{B}} = \frac{3}{2}$