The temperature of an ideal gas is increased from $200\,K$ to $800\,K$. If r.m.s. speed of gas at $200\,K$ is $v_0$. Then, r.m.s. speed of the gas at $800\,K$ will be:
A$v _0$
B$4 v_0$
C$\frac{v_0}{4}$
D$2 v _0$
JEE MAIN 2023, Easy
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D$2 v _0$
d $V _{ rms }=\sqrt{\frac{3 RT }{ M }}$
$\Rightarrow V _{ rms } \alpha \sqrt{ T }$
Increasing temperature $4$ times, rms speed gets doubled.
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