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A gas bubble oscillate with a …

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A gas bubble oscillate with a time period T proportional to p,d,e where p is preesure , d is density and e is energy. Find the valve of t.

Posted by Hemant Singh 7 years, 3 months ago

Entrance Exam > NEET-UG > Physics

1 answers

Naveen Sharma 7 years, 3 months ago

Given {tex}T = k p^a d^b E^c{/tex}

where k is a proportionally constant.
Substituting the dimensions of T, p, d and E,
we have
{tex} [T] = [[ML^{-1}T^{-2}]^ a [ML^{-3}]^ b [ML^2T^{ -2}]^ c {/tex}

Equating power of M, L, and T on both sides, we have
a + b + c = 0
–a –3b + 2c = 0
–2a – 2c = 1
Solving these equations, we get {tex}a = {-5\over 6}, \ b = {1\over 2} \ and \ c ={ 1\over 3}{/tex}

4Thank You

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Entrance Exam > NEET-UG > Physics