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Two spheres of radii in the ratio $2 : 3$ have specific heats in the ratio $3 : 4$ .
Their densities are in the ratio $4 : 5$ then the ratio of their water equivalents

are

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2 : 5

8 : 45

4 : 15

45 : 8

answer is C.

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Detailed Solution

r_{1} : r_{2} = 2 : 3

$s_{1} : s_{2} = 3 : 4$

$V_{1} = \frac{4}{3} π r^{3}$

$d_{1} : d_{2} = 4 : 5$

$= \frac{4}{3} π 27$

$w = dvs$

$\frac{w_{1}}{w_{2}} = \frac{d_{1} v_{1} s_{1}}{d_{2} v_{2} s_{2}}$

$\frac{4 \times \frac{4}{3} π \times 8 \times 3}{5 \times \frac{4}{3} \times π \times 27 \times 4} = \frac{8}{45}$

$w_{1} : w_{2} = 8 : 45$

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