Question:
An observer $A$ sees an asteroid with a radioactive element moving by at a speed $=0.3\, c$ and measures the radioactivity decay time to be $T_{A}$. Another observer $B$ is moving with the asteroid and measures its decay time as $T_{B} .$ Then $T_{A}$ and $T_{B}$ are related as
An observer $A$ sees an asteroid with a radioactive element moving by at a speed $=0.3\, c$ and measures the radioactivity decay time to be $T_{A}$. Another observer $B$ is moving with the asteroid and measures its decay time as $T_{B} .$ Then $T_{A}$ and $T_{B}$ are related as
Updated On: Apr 26, 2024
- $T_{B} < T_{A}$
- $T_{A}=T_{B}$
- $T_{B} > T_{A}$
- Either (A) or (C) depending on whether the asteroid is approaching or moving away from A
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The Correct Option is C
Solution and Explanation
Observers in different inertial frames always measure different time intervals between a pair of events. According to time dilation
$T_{A} > T_{B}$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.