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. `6.28 xx 10^(7)` m/s
D. `3.14 xx 10^(7)` m/s

Answer

D

Explanation

`T = (2pi r)/(v_("max")) implies v_("max") = (2pi r)/(T) = 2pi r f `
`implies 2 xx 3.14 xx 10^(7) xx 50 xx 10^(-2)`
`implies 3.14 xx 10^(7)` m/s