A proton and an alpha -particle, having kinetic energies K _{ p } and K _{alpha}, respectively, enter into a magnetic field at right angles.

Q: A proton and an $\alpha$ -particle, having kinetic energies $K _{ p }$ and $K _{\alpha},$ respectively, enter into $a$ magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $\alpha$ -particle is $2: 1 .$ The ratio of $K _{ p }: K _{\alpha}$ is :

d $r =\frac{ mv }{ qB }=\frac{ p }{ qB } \quad \frac{ m _{\alpha}}{ m _{ p }}=4$ $\frac{ r _{ p }}{ r _{\alpha}}=\frac{ p _{ p }}{ q _{ p }} \frac{ q _{\alpha}}{ p _{\alpha}}=\frac{2}{1}$ $\frac{ p _{ p }}{ p _{\alpha}}=\frac{2 q _{ p }}{ q _{\alpha}}=2\left(\frac{1}{2}\right)$ $\frac{ p _{ p }}{ p _{\alpha}}=1$ $\frac{ K _{ p }}{ K _{\alpha}}=\frac{ p _{ p }^{2}}{ p _{\alpha}^{ p }} \frac{ m _{\alpha}}{ m _{ p }}=(1)$ (4)

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A proton and an $\alpha$ -particle, having kinetic energies $K _{ p }$ and $K _{\alpha},$ respectively, enter into $a$ magnetic field at right angles.

The ratio of the radii of trajectory of proton to that of $\alpha$ -particle is $2: 1 .$ The ratio of $K _{ p }: K _{\alpha}$ is :

A$1:8$
B$8:1$
C$1:4$
D$4:1$

JEE MAIN 2021, Medium

STD 11 Science
NEET
STD 12 - 4. Moving charges and magnetism
Physics

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