Mark the correct statements: 1. Equations of special relativity are not applicable for small speeds. 2. Equations of special relativity are applicable for all speeds. 3. Nonrelativistic equations give exact result for small speeds. 4. Nonrelativistic equations never give exact result.

Mark the correct statements: 1. Equations of special relativity a…

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MCQ

Mark the correct statements:

Equations of special relativity are not applicable for small speeds.
Equations of special relativity are applicable for all speeds.
Nonrelativistic equations give exact result for small speeds.
Nonrelativistic equations never give exact result.

A
$a$ and $b$
✓
$b$ and $d$
C
$a$ and $c$
D
$b$ and $c$

✓

Answer

Correct option: B.

$b$ and $d$

According to special relativity, if a particle is moving at a very high speed $v$, its mass:
$\text{m}=\gamma\text{ m}_0,$length $\text{l}=\frac{\text{l}_0}{\gamma}, $ change in time $\triangle\text{t}=\gamma\ \triangle\text{t}_0$
where, $\gamma=\frac{1}{\sqrt{1-\frac{\text{v}^2}{\text{c}^2}}}\text{i}\text{f}\ \text{v}<<\text{c}$
$\Rightarrow\gamma\cong1$
that is at non relativistic speed (small speed), $\text{m}\cong\text{m}_0,\text{l}\cong\text{l}_0,\triangle\text{t}\cong\triangle\text{t}_0$
where $\text{m}_0,\text{l}_0$ and $\triangle\text{t}_0$ are the rest mass, length and time interval respectively. Therefore, relativistic equations are applicable for all speeds. But
$\gamma=\Big(1-\frac{\text{v}^2}{\text{c}^2}\Big)^{-\frac{1}{2}}$
$\Rightarrow\gamma=1+\frac{\text{v}^2}{\text{2c}^2}+\cdots ($expanding binomially$)$
$\frac{\text{v}^2}{2\text{c}^2}+\cdots=\text{K}<<1$ if $\text{v}<<\text{c}$ but silll $\text{K}>0$
Hence. non relativistic equations. in which $\curlyvee$ factor is taken to be exactly $1$ never give exact results.

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