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Q.

A proton is projected from the origin making an angle of 60° with the x-axis. A magnetic field B→=2i^ tesla exists in that region of space. The proton passes through the x-axis for the first time at a distance of 50 cm from the origin. When an α - particle is projected from the origin with same speed making an angle of 30° with the x-axis in the same magnetic field, it passes though the x-axis at a distance ‘d’ from the origin. Then the value of ‘d’ is

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a

103 cm

b

1003 cm

c

2003 cm

d

203 cm

answer is B.

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Detailed Solution

Trajectory of the proton or α - particle is helix whose pitch is given by p=2πmVcosαQB∴pαpp=mαmp QpQα (cos α)α(cos α)p⇒d50=(4)12cos 300cos 60o ⇒d = 1003 cm
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