If rate of diffusion of $A$ is $5$ times that of $B$ , what will be the density ratio of $A$ and $B$ ?

\frac{1}{25}

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\frac{1}{5}

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25

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5

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Solution

The correct option is B $\frac{1}{25}$
$r_{A} = 5 r_{B}$ , the rate of diffusion of a gas is inversely proportional to the square root of its' density.
$\frac{r_{A}}{r_{B}} = \sqrt{\frac{d_{B}}{d_{A}}}$
$\frac{5 r_{B}}{r_{B}} = \sqrt{\frac{d_{B}}{d_{A}}} ⟹ \frac{d_{B}}{d_{A}} = \frac{25}{1}$
Or, $\frac{d_{A}}{d_{B}} = \frac{1}{25}$

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Simplified value of $(25)^{\frac{1}{3}} \times 5^{\frac{1}{3}}$

(a) 25 (b) 3 (c) 1 (d) 5

Choose the correct answer in each of the following :

If the volumes of two cones be in the ratio 1:4 and the radii of their bases be in the ratio 4:5 then ratio of their heights is

(a) 1:5 (b) 5:4 (c) 25:16 (d) 25:64

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