Question

Two particle of mass in the ratio 1 : 2 with charges in the ratio q1 : q2 = 1:1are placed in a uniform electric field . They are relaxed and allowed to move for the same time .the ratio of their kinetic energy will be finally

Answer 1

answer : 2 : 1

as it is given that charge on both particles is same , so electric force applied on both of them will be same.

Let us consider , F is electric force acting on each of them.

so, linear momentum = impulse = force × time.

but it is given that they are relaxed and allowed to move for the same time.

so, linear momentum of both particles is also same.

now kinetic energy = linear momentum²/2 × mass

but linear momentum remains constant so, kinetic energy is inversely proportional to mass.

so, Ratio of kinetic energy , $\frac{K_1}{K_2}=\frac{m_2}{m_1}$

= $\frac{1}{\frac{m_1}{m_2}}$

given, $\frac{m_1}{m_2}=\frac{1}{2}$

so, $\frac{K_1}{K_2}=\frac{2}{1}$