Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as
Assertion 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. Reason Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field \[\mathbf{\vec{B}}\] in a direction perpendicular to \[\mathbf{\vec{B}}\], will describe circular trajectories of equal radii.A) If the Assertion and Reason are true and Reason is the correct explanation of Assertion.
B) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C) If Assertion is true but Reason is false.
D) If both Assertion and Reason are false.
Correct Answer: C
Solution :
The radius of the circular path is given by \[r=\frac{mv}{qB}=\frac{\sqrt{2mK}}{qB};\]where \[K=\frac{1}{2}m{{v}^{2}}\] Since K and B are the same for the t particles, \[r\propto \frac{\sqrt{m}}{q}.\] Now, the charge of an alpha particle is twice that of a proton and its mass is four times the mass of a proton, \[\sqrt{m}/q\] will be the same for both particles. Hence, r will be same for both particles.
You need to login to perform this action.
You will be redirected in
3 sec
