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Dimensions of a physical quantity

A gas bubble, from an explosion under water, oscillates with a

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Solving time: 2 mins

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 $c$ .

Views: 5,580 students

Updated on: Oct 13, 2023

Book:

Mechanics Volume 1 (DC Pandey)

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Henry Discussed

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

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

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

Equating the powers of both sides, we have

a + b + c = 0

- a - 3 b + 2 c = 0

- 2 a - 2 c = 1

Solving these three equations, we have

a = - \frac{5}{6}, b = \frac{1}{2}

and c = \frac{1}{3}

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Question Text	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 $c$ .
Updated On	Oct 13, 2023
Topic	Physical World
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 10
Upvotes	1065
Avg. Video Duration	7 min

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 $c$ .

Text solutionVerified

Filo tutor solutions (10)

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Text solutionVerified

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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 $c$ .