A proton a deutron and an `alpha` particle are accelerated through potentials of `V, 2V` and `4V` respectively. Their velocity will bear a ratio

Options

A. `1 : 1: 1`
B. `1: sqrt(2) : 1`
C. `sqrt(2): 1: 1`
D. `1: 1: sqrt(2)`

Answer

D

Explanation

If a charge q is accelerated through a p.d. of V volts then velocity v is given then
`1/2 mv^2= qv implies v=sqrt((2qV)/m) implies v_p: v_d: v_a =sqrt((2 eV)/m), sqrt((2e(2v))/m), sqrt(((2e)(4v))/(4m)), 1:1 sqrt2`