v_1 and v_2 are the velocities of sound at the same temperature i… - Vidyadip

MCQ

${v_1}$ and ${v_2}$ are the velocities of sound at the same temperature in two monoatomic gases of densities ${\rho _1}$ and ${\rho _2}$ respectively. If $\frac{\rho _1}{\rho _2} = \frac{1}{4}$ then the ratio of velocities ${v_1}$ and ${v_2}$ will be

A
$1:2$
B
$4:1$
✓
$2:1$
D
$1:4$

✓

Answer

Correct option: C.

$2:1$

c
(c) At given temperature and pressure

$v \propto \frac{1}{{\sqrt \rho }}$

==>$\frac{{{v_1}}}{{{v_2}}} = \sqrt {\frac{{{\rho _2}}}{{{\rho _1}}}} = \sqrt {\frac{4}{1}} = 2:1$

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