Home
Class 11
PHYSICS
A gas bubble, from an exlosion under wat...

A gas bubble, from an exlosion 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 `'E'` is the total energy of the explosion. Find the values of `a, b and, c`.

Text Solution

Verified by Experts

The correct Answer is:
(a) `= -5//6 , b = 1//2 , c = 1//3`
Given that `T prop P^(a) a^(b) E^( c )`
`[ M^(0) L^(0) T^(1) ] = [ ML^(-1) T^(-2)]^(a) [ML^(-3)]^(b) [ML^(2) T^(-2)]^( c )`
`[M^(0) L^(0) T^(1)] = [ M^(a + b + c ) L^( -a - 3b + 2 c) T^( -2a -2 c )] a + b + c = 0`
`-a - 3b + 2 c = 0 -2a -2c = 1`
On solving , we get
`a = - 5//6 , b = 1//2 , c = 1//3`
`T prop P^(-5//6) d^(1//2) E^(1//3)`
`T = kp ^(-5//6) d^(1//2) E^(1//3)`
where `k` is the proportionality constant.
Promotional Banner

Topper's Solved these Questions

  • DIMENSIONS & MEASUREMENT

    CENGAGE PHYSICS|Exercise Fill In The Blanks|4 Videos

  • DIMENSIONS & MEASUREMENT

    CENGAGE PHYSICS|Exercise Single correct Answer Type|15 Videos

  • DIMENSIONS & MEASUREMENT

    CENGAGE PHYSICS|Exercise Linked Comprehension|3 Videos

  • CENTRE OF MASS

    CENGAGE PHYSICS|Exercise INTEGER_TYPE|1 Videos

  • FLUID MECHANICS

    CENGAGE PHYSICS|Exercise INTEGER_TYPE|1 Videos

Similar Questions

Explore conceptually related problems

A gas bubble, from an exlosion 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 is the total energy of the explosion. Find the values of a, b and, c .

A gas bubble , from an explosing under water , oscillates with a period T proportional in P^(0)D^(0)E^(0) , where p is the static prossure , d is the density of water and E is the total energy of the explosion . Find the value of a , b and c .

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 pressure, d is density of water and E is the total energy of the explosion. Find the value of a,b and c .

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

A gas bubble oscillates with a time period T proportional to p^(a) d^(b) E^(c) where P is pressure , d is the density and E is the energy. The values of a,b and C are :

A dubble under water oscillates with period T, which is proportional to p^(-5//6),d^(1//2)E^(Y), where p is pressure, d is density and E is energy. The value of gamma is -

The period T of a soap bubble under SHM 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 time period of a body undergoing simple harmonic motion is given by T = p^a D^b S^c , where p is the pressure, D is density and S is surface tension. The values of a, b and c respectively are

If the period 'T' of a drop under surface tension 's' is given by T = sqrt(d^(a) r^(b) S^(c)) where d is the density , r is the radius of the drop. If a=1,c= -1 then the value of b is

If the numbers a, b, c, d, e are in arithmetic progression then find the value of a - 4b + 6c - 4d + e.