Assertion: A proton an an alpha particle having the same kinetic energy are moving in circular paths in a unifrom magnetic field. The radii of their circular paths wll be equal.
Reason: Any two charged particles having equal kinetic energies and entering a region of unifrom magnetic feild `vec(B)` in a direction perpendicular to `vec(B)`, will describe circular trajectoreis of equal radii.

Options

A. If both the assertion and reason are true and reason is a true explantion of the assertion.
B. If both the assertion and reason are true but the reason is not the correct explantion of the assertion.
C. If the assertion is true but reason false
D. If both the assertion and reason are false.

Answer

A

Explanation

The ratio of the circular path is given by
`r = (mv)/(qB) = (sqrt(2mK))/(qB)` , where `K = (1)/(2) mv^(2)`
Since `K` and `B` are the same for the two particles, `r prop (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 body particles. Hence, `r` will be the same for both particles.