The period $T$ of a soap bubble under $S H M$ is given by $T = P^{a} D^{b} S^{c}$ , where $P$ is pressure, $D$ , is density and $S$ is surface tension. Then the values of $a, b$ and $c$ are

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

$- 1, - 2, 3$

$\frac{1}{3}, - \frac{3}{2}, - 1 / 2$

$1, 2, \frac{3}{2}$

Video Solution

Text Solution

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The correct Answer is:A

(1) $T = P^{a} D^{b} S^{c}$
$T = {[M L^{- 1} T^{- 2}]}^{a} {[M L^{- 3}]}^{b} {[M T^{- 2}]}^{c}$
$M^{0} L^{0} T^{- 1} = M^{a + b + c} L^{- a - 3 b} T^{- 2 a - 2 c}$
$a + b + c = 0$
$- a - 3 b = 0$
$- 2 a - 2 c = 1 \Rightarrow a + c = - \frac{1}{2}$
$b = \frac{1}{2}, a = - \frac{3}{2}, c = 1$
$a = - \frac{3}{2}, b = \frac{1}{2}, c = 1$

Updated on:21/07/2023

Class 11 PHYSICS DIMENSION AND MEASUREMENT

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The period $T$ of a soap bubble under $S H M$ is given by $T = P^{a} D^{b} S^{c}$ , where $P$ is pressure, $D$ , is density and $S$ is surface tension. Then the values of $a, b$ and $c$ are

The correct Answer is:A

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