The ratio of the masses and charges of a proton and an alpha particle are respectiely `1:4 and 1:2`. They enter a uniform magnetic field of magnitude B normally with same kinetic energy. What will be the ratio of the radii of the circular paths described by the particles in each case ?

Explanation

Radius ofhte circular path `r=(mv)/(qB),B` = constant.
`r=(mv)/(qB)= (sqrt((1)/(2)mv^(2)*2m))/(qB)`
If kinetic energy `(1)/(2)mv^(2)` is the same then `r prop (sqrt(m))/(q)`
`:. (r_(1))/(r_(2))= sqrt((m_(1))/(m_(2)))xx(q_(2))/(q_(1))= sqrt((1)/(4))xx(2)/(1)=(1)/(1)`