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A proton, a deuteron and an alpha particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is__ and their speed is _ in the ratio.

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a

1:2:4 and 2:1:1

b

1:2:4 and 1:1:2

c

4:2:1 and 2:1:1

d

2:1:1 and 4:2:1

answer is D.

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Detailed Solution

Magnetic Force, F=qvB=qPBmhere, v=Pm⇒F ∝ qm⇒v ∝ 1m⇒F1:F2:F3=q1m1:q2m2:q3m3⇒v1:v2:v3=1m1:1m2:1m3⇒F1:F2:F3=qm:q2m:2q4m⇒v1:v2:v3=1m:12m:14m⇒F1:F2:F3=2:1:1⇒v1:v2:v3=4:2:1

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