A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :

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1 : 4

2 : 1

1 : 2

1 : 1

answer is C.

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Detailed Solution

radius of particle in cyclotron
$r = \frac{\sqrt{2 m (K \cdot E .)}}{qB}$
So ratio of new radius to original
$\frac{r_{n}}{r_{0}} = \sqrt{\frac{(K.E.)_{n}}{(K . E)_{0}}} = \sqrt{4} = 2$

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