The time period T of simple pendulum depends upon length l of the pendulum and gravitational acceleration. The formula for time period of simple pendulum is given by

Question

Infinity Learn · Accepted Answer

Let T∝la     and   T∝gbwhere a and b are dimensionless $$constantsT=klagbwhere$$, k is dimensionless constant.[LHS][T]$$=$$[$$M0L0T$$−$$1$$]and [RHS]$$(lagb)=$$[L]a[LT−$$2$$]$$b=$$[$$La+bT$$−$$2b$$]$$=$$[$$M0La+bT$$−$$2b$$]According to homogeneity principle,[LHS] $$=$$ [RHS]or [$$M0L0T$$]$$=$$[$$M0La+bT$$−$$2b$$]For dimensional balance, dimensions on both sides should be same.∴   $$a+b=0and$$ $$-2b$$ $$=1$$∴           $$b=$$−$$12and$$ $$a=12$$∴       $$T=2$$$$π$$lg[since, numerical value of k in case of simple pendulum is $$2$$π]

The time period T of simple pendulum depends upon length l of the pendulum and gravitational acceleration. The formula for time period of simple pendulum is given by

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