A gas bubble from an explosion under water oscillates with a time period T, depends upon static pressure p, density of water r and the total energy of explosion E. The expression for the time period T. (where, k is a dimensionless constant) is

Time period,T∝paρbEcor T=kpaρbEck, is a dimensionless constant.According to homogeneity of dimensions,LHS = RHS∴      [T]=[ML−1T−2]a[ML-3]b[ML2T−2]c[T]=[Ma+b+c][L−a−3b+2c][T−2a−2c]Comparing the powers, we obtaina + b + c = 0-a -3b + 2c = 0-2a -2c =1On solving, we geta=56,  b=12,c=13