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