The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density () of liquid and the surface tension (s) of the liquid as : . The values of a, b and c respectively are [2023]

Question

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 [2023]

Smart Achievers · Accepted Answer

(2)

$[T^{- 1}] = {[L^{1}]}^{a} {[M^{1} L^{- 3}]}^{b}$ ${[\frac{{MLT}^{- 2}}{L}]}^{c}$

$\Rightarrow T^{- 1} = M^{b + c} \cdot L^{a - 3 b} \cdot T^{- 2 c}$

$c = \frac{1}{2}, b = - \frac{1}{2}, a - 3 b = 0$

$a + \frac{3}{2} = 0 \Rightarrow a = - \frac{3}{2}$

Solution

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 [2023]

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

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

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

4 $(\frac{3}{2}, - \frac{1}{2}, \frac{1}{2})$

Ans.
(2)

$[T^{- 1}] = {[L^{1}]}^{a} {[M^{1} L^{- 3}]}^{b}$ ${[\frac{{MLT}^{- 2}}{L}]}^{c}$

$\Rightarrow T^{- 1} = M^{b + c} \cdot L^{a - 3 b} \cdot T^{- 2 c}$

$c = \frac{1}{2}, b = - \frac{1}{2}, a - 3 b = 0$

$a + \frac{3}{2} = 0 \Rightarrow a = - \frac{3}{2}$

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Solution

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=raρbsc. The values of a, b and c respectively are [2023]

1 (–32,12,12)

2 (–32,–12,12)

3 (32,12,–12)

4 (32,–12,12)

Ans. (2) [T–1]=[L1]a[M1L–3]b[MLT-2L]c ⇒ T–1=Mb+c·La–3b·T–2c c=12, b=–12, a–3b=0 a+32=0 ⇒ a=–32