Correct Answer  Option 1 : 8 ∶ 1
The correct answer is option 1) i.e. 8 ∶ 1
CONCEPT:
 The electric field is defined as the electric force per unit charge.
 A stationary charge q placed in an electric field intensity of E will experience an electrostatic force (F) given by
F = qE
 If a particle of mass m accelerates, from Newton's second law we know that the force experienced by this particle, F = ma
 For a charged particle the force experienced, F = qE
Therefore, qE = ma
⇒ Acceleration, a = qE/m

Kinetic energy is the energy possessed by a moving object. It is given by
KE = \(\frac{1}{2}\)mv^{2}
EXPLANATION:
Let the mass of two particles have mass m_{1} and m_{2} and charge q1 and q2.
m_{1} = m ; q_{1} = 2q
m_{2} = 2m ; q_{2} = q
We know that acceleration = velocity ÷ time ⇒ v = at
v_{1} = a_{1}t = q_{1}Et/m_{1}
v_{2} = a2t = q2Et/m2
The kinetic energy of the particles will be as follows
KE_{1} = \(\frac{1}{2}m_1v_1^2 = \frac{1}{2}(m)(\frac{(2q)E}{m} t)\)
KE2 = \(\frac{1}{2}m_2v_2^2 = \frac{1}{2}(2m)(\frac{qE}{2m} t)\)
Ratio = \(\frac{KE_1}{KE_2} = \)\(\frac{\frac{1}{2}(m)(\frac{2qE}{m} t)^2}{\frac{1}{2}(2m)(\frac{qE}{2m} t)^2} =\frac{2^2 / 1}{2/2^2} = \frac{4/1}{2/4} = \frac{16}{2} = \frac{8}{1} \)
Therefore, the ratio of the kinetic energies is 8 : 1.