# Solve this

Question:

A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces action on them is______ and their speed is_______ in the ratio.

1. $2: 1: 1$ and $4: 2: 1$

2. $1: 2: 4$ and $2: 1: 1$

3. 1: $2: 4$ and 1: 1:2

4. 4: $2: 1$ and $2: 1: 1$

Correct Option: 1

Solution:

(1)

As $v=\frac{p}{m} \& F=q v B$

$\therefore F=\frac{q p}{m} B$

$F_{1}=\frac{q p B}{m}, v_{1}=\frac{p}{m}$

$F_{2}=\frac{q p B}{2 m}, v_{2}=\frac{p}{2 m}$

$F_{3}=\frac{2 q p B}{4 m}, v_{3}=\frac{p}{4 m}$

$F_{1}: F_{2}: F_{3} \& V_{1}: V_{2}: V_{3}$

$\begin{array}{ll}1: \frac{1}{2}: \frac{1}{2} & \& 1: \frac{1}{2}: \frac{1}{4} \\ 2: 1: 1 & \& 4: 2: 1\end{array}$