Two particles X and Y, of equal mass and with | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the masses be $m$ and charges be $q_1$ and $q_2$. Initially, $X$ has velocity $u$ and $Y$ is at rest. The total momentum of the system is $P_i

Vedclass · Accepted Answer

both will move with velocities  <  $u/2$.

Vedclass · Answer

(D) Let the masses be $m$ and charges be $q_1$ and $q_2$. Initially, $X$ has velocity $u$ and $Y$ is at rest. The total momentum of the system is $P_i = mu + m(0) = mu$.Since the particles are far apart initially, the potential energy is zero. As $X$ approaches $Y$, the repulsive electrostatic force acts on both particles.By the law of conservation of linear momentum, the total momentum remains constant: $m v_X + m v_Y = mu$, which implies $v_X + v_Y = u$.By the law of conservation of energy, the initial kinetic energy $K_i = \frac{1}{2}mu^2$ is converted into final kinetic energy and potential energy: $\frac{1}{2}mu^2 = \frac{1}{2}mv_X^2 + \frac{1}{2}mv_Y^2 + U_f$, where $U_f > 0$.Since $U_f > 0$, the sum of final kinetic energies must be less than the initial kinetic energy: $\frac{1}{2}m(v_X^2 + v_Y^2) Given $v_X + v_Y = u$, if $v_X = 0$, then $v_Y = u$, which would mean $v_X^2 + v_Y^2 = u^2$, contradicting the energy conservation with $U_f > 0$. Thus, $v_X$ cannot be $0$. Both particles will continue to move with velocities such that their sum is $u$ and their individual velocities are less than $u/2$.

Two particles $X$ and $Y$, of equal mass and with unequal positive charges, are free to move and are initially far away from each other. With $Y$ at rest, $X$ begins to move towards it with initial velocity $u$. After a long time, finally

Similar Questions

Point charges are placed at the vertices of a regular hexagon with center $O$ and side length $L$ as shown in the figure. Given $K = \frac{q}{4\pi \epsilon_0 L^2}$,which of the following statements is correct?

What is the angle between the strings and the tension in the strings when two spheres are suspended in a satellite as shown in the figure?

For two electrons separated by a distance of $10 \, cm$,let $F_g$ and $F_e$ represent the gravitational force and electrostatic force between them,respectively. The ratio $F_g / F_e$ is of the order of:

For the given figure,the direction of the electric field at point $A$ will be .........

Three parallel metal plates,each of area $A$,are placed as shown in the figure. Charges $Q_1$,$Q_2$,and $Q_3$ are given to them. Edge effects are negligible. Calculate the charge on the two outermost surfaces '$a$' and '$f$'.

Vedclass Test Series

Exam Paper Generator

Online Exam Module