An electron having kinetic energy $T$ is moving in a circular orbit of radius $R$ perpendicular to a uniform magnetic induction $\vec B$ . If kinetic energy is doubled and magnetic induction tripled, the radius will become
A$\frac{{3\,R}}{2}$
B$\sqrt {\frac{3}{2}} \,R$
C$\sqrt {\frac{2}{9}} \,R$
D$\sqrt {\frac{4}{3}} \,R$
Medium
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C$\sqrt {\frac{2}{9}} \,R$
c $r=\frac{m v}{q B}=\sqrt{\frac{2 m T}{q B}}$
$r^{\prime}=\frac{\sqrt{2 m(2 T)}}{q(3 B)}=\frac{\sqrt{2}}{3} r \Rightarrow \sqrt{\frac{2}{9}} R$
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