Two identical charged particles enter a uniform magnetic field with same speed but at angles `30^(@)` and `60^(@)` with field Let a,b and c be the ratio of their time periods, radii and pitches of the helical paths than .

Options

A. `abc=1`
B. `abc gt 1`
C. `abc lt 1`
D. a= bc

Answer

A

Explanation

Ratio of time periods, `a= (T_(1))/(T_(2)) = (2pi m//qB)/(2pi m//qB) =1`
Ratio of radii, `b= (mv sin 30^(@)//qB)/(mv sin 60^(@)//qB)= tan 30^(@)`
Ratio of pitches, `c= (v sin 60^(@)T)/(v sin 30^(@)T) xx T = tan 60^(@)`
`:. bc= 1=a rArr abc= 1`