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

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Infinity Learn · Accepted Answer

Time period,T∝paρbEcor $$T=kpa$$ρbEck, 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 $$geta=56$$,  $$b=12$$,$$c=13$$

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

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