| ASSERTION: A charged particle moving in a uniform magnetic field penetrates a layer of lead and thereby loses half of its kinetic energy. The radius of curvature of its path is now reduced to half of its initial value. |
| REASON: Kinetic energy is inversely proportional to radius of curvature. |
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true and 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.
E) If assertion is false but reason is true.
Correct Answer: D
Solution :
The radius of curvature of charged particle in a magnetic field is given by, \[r=\frac{mv}{qB}=\frac{\sqrt{2m.\,K.E.}}{qB}\] I.e. \[r\propto \sqrt{K.E.}\]when kinetic energy is halved, the radius is reduced to \[\left( \frac{1}{\sqrt{2}} \right)\]times its initial value.
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