Two electrons one moving in opposite direction with speeds 0.8 c and 0.4 c where c is the speed of light in vacuum. Then the relative speed is about

Correct answer: (C) 0.9 c. Relative speed is given by u=fracu^′+v1+fracu^′ vc^2 Here, u^′=0.8 c and v=0.4 c ∴ u=frac0.8 c+0.4 c1+frac(0.8 c)(0.4 c)c^2=(1.2 c)/1.32=0.9 c

Q87 / 120 · VITEEE 2007 · Physics

Two electrons one moving in opposite direction with speeds $0.8 \mathrm{c}$ and $0.4 \mathrm{c}$ where $\mathrm{c}$ is the speed of light in vacuum. Then the relative speed is about

A
$0.4 \mathrm{c}$
B
$0.8 \mathrm{c}$
Correct answer
C
$0.9 \mathrm{c}$
D
$1.2 \mathrm{c}$

Solution

Relative speed is given by $u=\frac{u^{\prime}+v}{1+\frac{u^{\prime} v}{c^{2}}}$ Here, $u^{\prime}=0.8 \mathrm{c}$ and $\mathrm{v}=0.4 \mathrm{c}$ $\therefore \mathrm{u}=\frac{0.8 \mathrm{c}+0.4 \mathrm{c}}{1+\frac{(0.8 \mathrm{c})(0.4 \mathrm{c})}{\mathrm{c}^{2}}}=\frac{1.2 \mathrm{c}}{1.32}=0.9 \mathrm{c}$

Hence, the correct answer is option: 'C'.

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