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Q.

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

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a

a=32,b=−13,c=12

b

a=−52,b=13,c=12

c

a=−56,b=12,c=13

d

a=32,b=−1,c=12

answer is C.

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Detailed Solution

[T]=[P]a[d]b[E]c M0L0T1=(ML−1T−2)a(ML−3)b(ML2T−2)c comparing dimensions on both sides we get⇒a+b+c=0 −a−3b+2c=0 −2a−3b−2c=1 solving we get a=−56,b=12,c=13
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