Question

Given that the time period t of ossicilation of a gas bubble from an explosion

Answer 1

I think that answar I s 50

Answer 2

a=−56,b=12andc=13

Explanation:

Given time period T

   T∝p^ad^bE^c

   T=Kp^ad^bE^c.....(1)

   where K is a constant of proportionality and dimensionless quantity.

   [T]=[ML−1T−2]^a[ML−3]^b[ML2T−2]^c

Equating powers of M,L,andT on both sides we get

   0=a+b+c .....(2)

   0=–a–3b+2c .....(3)

   1=–2a–2c ......(4)

Solving these equations

From (4)

   a+c=−1/2 .....(5)

Inserting this value in (2)

   0=b−1/2

   ⇒b=1/2

From (5)

   a=−1/2−c

Inserting values of aandb in (3)

   0=−(−1/2−c)−3×1/2+2c

   ⇒3c=1

   ⇒c=1/3

Inserting value of c in (5)

   a+1/3=−1/2

   ⇒a=−1/2−1/3

   ⇒a=−5/6

           ∴a=−5/6,b=1/2andc=1/3

T∝p^-5/6 d^1/2 E^1/3