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Q.

The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density $(ρ)$ of liquid and the surface tension (s) of the liquid as : $v = r^{a} ρ^{b} s^{c}$ . The values of a, b and c respectively are

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a

$(- \frac{3}{2}, - \frac{1}{2}, \frac{1}{2})$

b

$(\frac{3}{2}, - \frac{1}{2}, \frac{1}{2})$

c

$(\frac{3}{2}, \frac{1}{2}, - \frac{1}{2})$

d

$(- \frac{3}{2}, \frac{1}{2}, \frac{1}{2})$

answer is A.

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Detailed Solution

$Let v = k r^{a} ρ^{b} s^{c} \dots (i) [M^{0} L^{0} T^{- 1}] = L^{a} {(M L^{- 3})}^{b} {(M T^{- 2})}^{c} [M^{0} L^{0} T^{- 1}] = M^{b + c} L^{a - 3 b} T^{- 2 a} ∴ b + c = 0 \dots (i i) a - 3 b = 0 \dots (i i i) - 2 c = - 1, ∴ c = \frac{1}{2} From (ii), b = - c = - \frac{1}{2} from (iii), a = 3 b = - \frac{3}{2}$

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