CBSE Class 12-science Answered

Please refer to the dimensional analysis for the solution.

The oscillations can be measured by frequency of oscillation.

T   P^aρ^bE^c   where, symbols have their usual meaning.

Writing in terms of dimensions,

[T] = [ML^-1T^-2]^a[ML^-3]^b[ML²T^-2]^c

Comparing the exponents of M:

0 = a+b+c ... (1)

Comparing exponents of T:

1 = -2a-2c

a+c = -1/2     .... (2)

Comparing exponents of L:

0 = -a-3b+2c  ... (3)

Using (2) in (1) gives,

b = 1/2,

Hence (3) becomes,

a - 2c = -3/2    .........(4)

Solving (2) and (4), we find,

c = 1/3 and a = -5/6.

Hence,

T = Cρ^1/2E^1/3/P^5/6

where C is a constant.

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