SATHEE: General Physics Question 28

General Physics Question 28

Question 28

A gas bubble, from an explosion under water, oscillates with a period $T$ proportional to $p^{a} d^{b} E^{c}$ , where $p$ is the static pressure, $d$ is the density of water and $E$ is the total energy of the explosion. Find the values of $a, b$ and $c$ .

(1981, 3M)

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Answer:

Correct Answer: 36. $a = \frac{- 5}{6}, b = \frac{1}{2}, c = \frac{1}{3}$

Solution:

$[T] = [p^{a} d^{b} E^{c}] = {[{ML}^{- 1} T^{- 2}]}^{a} {[{ML}^{- 3}]}^{b} {[{ML}^{2} T^{- 2}]}^{c}$

Equating the powers on both sides, we have

$\begin{aligned} a + b + c & = 0 - a - 3 b + 2 c & = 0 - 2 a - 2 c & = 1 \end{aligned}$

Solving these three equations, we have

$\begin{aligned} a & = - \frac{5}{6}, b = \frac{1}{2} and c & = \frac{1}{3} \end{aligned}$

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General Physics Question 28

Question 28

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