# A Rod of Rest Length L Moves at a Relativistic Speed. Let L' = L/γ. Its Length (A) Must Be Equal To L' (B) May Be Equal To L (C) May Be More Than L' but Less Than L (D) May Be More Than L - Physics

A rod of rest length L moves at a relativistic speed. Let L' = L/γ. Its length

(a) must be equal to L'
(b) may be equal to L
(c) may be more than L' but less than L
(d) may be more than L

#### Solution

(b) may be equal to L
(c) may be more than L' but less than L

If a rod of rest length L is moving at a relativistic speed v and its length is contracted to L', then

$L' = \frac{L}{\gamma} = L\sqrt{1 - \frac{v^2}{c^2}}$

If $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}},\text{ then }v < < c, \gamma \cong 1 .$

$\Rightarrow L' \cong L$

But the length of the rod may be more than L' depending on the frame of the observer. However, it cannot be more than L because as the speed of the rod increases, its length contracts more and more due to increasing value of gamma.

Concept: Energy and Momentum
Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 25 The Special Theory of Relativity
MCQ | Q 5 | Page 457