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Q.

Statement 1: A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.Statement 2: Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field B→ in a direction perpendicular to B→, will describe circular trajectories of equal radii.

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a

Both statements 1 and 2 are correct

b

Statement 1 is correct statement 2 is incorrect

c

Statement 1 is incorrect statement 2 is correct

d

Both statements 1 and 2 are incorrect

answer is B.

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Detailed Solution

The radius of the circular path is given byr=mvqB = 2mKqB ; where K=12 mv2Since K and B are the same for the two particles, r ∝ mq. Now, the charge of an alpha particle is twice that of a proton and its mass is four times the mass of a proton, m/q will be the same for body particles. Hence, r will be the same for both particles.

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Statement 1: A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.Statement 2: Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field B→ in a direction perpendicular to B→, will describe circular trajectories of equal radii.