Question

A large fluid star oscillates in shape under the influence of its own gravitational field. Using dimensional analysis find the expression for period of oscillation (T) in terms of radius of star (R), mean density of
fluid (p) and universal gravitational constant (G).​

Answer 1

We have T ∝ RalbGc or T = k.RalbGc here [T] = [M0L0T1] [R] = [M0L1T0] [l] = [M1L-3T0] [G] = [M-1L3T-2] so, we have [M0L0T1] = [M0L1T0]a.[M1L-3T0]b.[M-1L3T-2]c or [M0L0T1] = [Mb-c.La-3b+3c.T-2c] now, by comparing the two sides we get b - c = 0 or b = c a - 3b + 3c = 0 or a = 3(b-c) = 0 -2c = 1 or c = -1/2 so, b = -1/2 thus, from the first relation,

Answer 2

Answer:

T<<√1/pG

Explanation:

Refer the above attachment

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