Question

a gas bubble from an explosion under water oscillates with a period T propotional to p^a p^b E^c where p is the static prresure p is the density of water and E is the total energy of the explosion. find the value of a,b,c

Answer 1

Given T = k pa db Ec, where k is a proportionally constant. Substituting the dimensions of T, p, d and E, we have
(T) = (ML-1T-2) a (ML-3) b (ML2T -2) c
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 a = -5/6, b = 1/2 and c = 1/3

Answer 2

Given T = k p^a d^b E^c, where k is a proportionally constant. Substituting the dimensions of T, p, d and E, we have

(T) = (ML^-1T^-2) ^a (ML^-3)^ b (ML^2T ^-2) ^c

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 a = -5/6, b = 1/2 and c = 1/3