Two ions having masses in the ratio 1:1 and c | vedclass

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(A) The radius $r$ of a circular path of a charged particle moving in a uniform magnetic field $B$ is given by the formula $r = \frac{mv}{qB}$.Given t

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$4:3$

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(A) The radius $r$ of a circular path of a charged particle moving in a uniform magnetic field $B$ is given by the formula $r = \frac{mv}{qB}$.Given the ratios:Mass ratio: $\frac{m_1}{m_2} = \frac{1}{1}$Charge ratio: $\frac{q_1}{q_2} = \frac{1}{2}$Speed ratio: $\frac{v_1}{v_2} = \frac{2}{3}$Since the magnetic field $B$ is uniform and the same for both,the ratio of the radii is:$\frac{r_1}{r_2} = \left( \frac{m_1}{m_2} ight) 	imes \left( \frac{v_1}{v_2} ight) 	imes \left( \frac{q_2}{q_1} ight)$Substituting the given values:$\frac{r_1}{r_2} = \left( \frac{1}{1} ight) 	imes \left( \frac{2}{3} ight) 	imes \left( \frac{2}{1} ight) = \frac{4}{3}$Therefore,the ratio of the radii is $4:3$.

Two ions having masses in the ratio $1:1$ and charges in the ratio $1:2$ are projected into a uniform magnetic field perpendicular to the field with speeds in the ratio $2:3$. The ratio of the radii of the circular paths along which the two particles move is

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