The maximum velocity to which a proton can be accelerated in a cyclotron of 10 MHZ frequency and radius 50 cm is

Options

A. `6.28 xx 10^(8)` m/s
B. `3.14 xx 10^(8)` m/s
C. `3.14 xx 10^(7)` m/s
D. `6.28 xx 10^(7)` m/s

Answer

D

Explanation

v = 10 MHz = `10^(7)` Hz
r = 50 cm = 0.5 m
The maximum velocity of proton.
`v = 2 pi r v`
`= 2 pi xx 50 xx 10^(-2) xx 10^(-7)`
`v = 3.14 xx 10^(7) ms^(-1)`