Question

Two charged particles having masses in the ratio $2:3$ and charges in the ratio $1:2$ are released from rest in a unifrom electric field. After $1$ minute, the their $K.E$ will be in the ratio of

• A. $1:3$
• B. $2:5$
• C. $3:8$
• D. $3:4$

Answer 1

The correct option is C $3:8$

Given,

$m_1:m_2=2:3q_1:q_2=1:2$

Using kinematics equation
$v=u+at=0+\frac{Eq}{m}tv=\frac{Eq}{m}t$

$\frac{K{E}_1}{K{E}_2}=\frac{\frac{1}{2}{m}_1{v}_1^2}{\frac{1}{2}{m}_2{v}_2^2}=\frac{m_1\times q_1^2\times m_2^2}{m_2\times q_2^2\times m_1^2}$

$\frac{K{E}_1}{K{E}_2}=\frac{m_2{q}_1^2}{m_1{q}_2^2}=\left(\frac{3}{2}\right)\times \left(\frac{1}{4}\right)=\frac{3}{8}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (c) is the correct answer.