Question

A rocket (S') moves at a speed $\frac{c}{2}$m/s along the positive x-axis, where c is the speed of light. When it crosses the origin, the clocks attached to the rocket and the one with a stationary observer (S) located at x = 0 are both set to zero. If S observes an event at (x, t), the same event occurs in the S' frame at

• A. $x'=\frac{2}{\sqrt3}(x-\frac{ct}{2})\ \text{and}\ t'=\frac{2}{\sqrt3}(t-\frac{x}{2c})$
• B. $x'=\frac{2}{\sqrt3}(x+\frac{ct}{2})\ \text{and}\ t'=\frac{2}{\sqrt3}(t-\frac{x}{2c})$
• C. $x'=\frac{2}{\sqrt3}(x-\frac{ct}{2})\ \text{and}\ t'=\frac{2}{\sqrt3}(t+\frac{x}{2c})$
• D. $x'=\frac{2}{\sqrt3}(x+\frac{ct}{2})\ \text{and}\ t'=\frac{2}{\sqrt3}(t+\frac{x}{2c})$

Answer 1

The Correct Option is A

The correct answer is (A) : $x'=\frac{2}{\sqrt3}(x-\frac{ct}{2})\ \text{and}\ t'=\frac{2}{\sqrt3}(t-\frac{x}{2c})$