List of top Physics Questions on Relativity asked in IIT JAM PH

Consider a relativistic particle of rest mass 2m moving with a speed v along the x direction. It collides with another relativistic particle of rest mass m moving with the same speed but in the opposite direction. These two particles coalesce to form one particle whose rest mass M is
($\beta = \frac{v}{c}$, where c is the speed of light)

A particle is moving with a velocity $ 0.8c $ (where $ c $ is the speed of light) in an inertial frame $ S_1 $. Frame $ S_2 $ is moving with a velocity $ 0.8c $ with respect to $ S_1 $. Let $ E_1 $ and $ E_2 $ be the respective energies of the particle in the two frames. Then, $ \frac{E_2}{E_1} $ is ............ (Round off to two decimal places).

Three events, $ E_1(ct = 0, x = 0) $, $ E_2(ct = 0, x = L) $ and $ E_3(ct = 0, x = -L) $ occur, as observed in an inertial frame $ S $. Frame $ S' $ is moving with a speed $ v $ along the positive x-direction with respect to $ S $. In $ S' $, let $ t'_1, t'_2, t'_3 $ be the respective times at which $ E_1, E_2, $ and $ E_3 $ occurred. Then,

Two relativistic particles with opposite velocities collide head-on and come to rest by sticking with each other. Which of the following quantities is/are conserved in the collision?

Rod $R_1$ has rest length 1 m and rod $R_2$ has rest length 2 m. $R_1$ and $R_2$ move with velocities $+v\hat{i}$ and $-v\hat{i}$ respectively relative to the lab. If $R_2$ has a length of 1 m in the rest frame of $R_1$, $\frac{v}{c}$ is ................... (Specify answer up to two digits after decimal.)

Two events occur in frame $S$ at $(t_1 = 0,\ r_1 = 0)$ and $(t_2 = 0,\ x_2 = 10^8\mathrm{m}, y_2 = 0, z_2 = 0)$. Another frame $S'$ moves with $v = 0.8c$ relative to $S$. The time difference $(t_2' - t_1')$ in $S'$ is ................... s. (Specify answer up to two digits after decimal.)

Consider an inertial frame $ S' $ moving at speed $ c/2 $ away from another inertial frame $ S $ along the common x-axis, where $ c $ is the speed of light. As observed from $ S' $, a particle is moving with speed $ c/2 $ in the $ y' $ direction, as shown in the figure. The speed of the particle as seen from $ S $ is: