A gas bubble formed from an explosion under water oscillates with a period T proportional to padbEc, where p is the pressure, d is the density of water and E is the total energy of explosion. The values of a, b and c are

Given, T∝padbEcWe have, M0 L0 T=kML-1 T-2aML-3bML2 T-2cwhere, k is a constant.⇒M0 L0 T=kMa+b+c L-a-3b+2c T-2a-2cOn comparing powers of M, we have0=a+b+c    .....(i)On comparing powers of L, we have0=-a-3b+2c    .....(ii)On comparing powers of T, we have1=-2a-2c    .....(iii)On solving Eqs. (i), (ii) and (iii), we havea = -56, b =12, c = 13