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Q.

A charged particle is projected with velocity v in a uniform magnetic field making an angle of 450 with the field. The particle followed a helical path of radius 10 cm. If the same particle is projected with velocity 2V in the same magnetic field making an angle of 600 with the field, radius of helical path followed by the particle will be

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a

106  cm

b

103  cm

c

206  cm

d

10 cm

answer is A.

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Detailed Solution

(1)r=V sinθω=V sinθQB/m∴   r ∝  V sinθ ∴   r10=2V sin600V sin450   ⇒  r=106  cm
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A charged particle is projected with velocity v in a uniform magnetic field making an angle of 450 with the field. The particle followed a helical path of radius 10 cm. If the same particle is projected with velocity 2V in the same magnetic field making an angle of 600 with the field, radius of helical path followed by the particle will be