If the time period (T) of vibration of a liqu | vedclass

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(A) Let the time period $T$ be proportional to $S^x r^y \rho^z$,so $T = k S^x r^y \rho^z$.Substituting the dimensions:$[T] = [M^0 L^0 T^1]$$[S] = [M L

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$T = k\sqrt{\rho r^3/S}$

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(A) Let the time period $T$ be proportional to $S^x r^y \rho^z$,so $T = k S^x r^y \rho^z$.Substituting the dimensions:$[T] = [M^0 L^0 T^1]$$[S] = [M L^0 T^{-2}]$$[r] = [L]$$[\rho] = [M L^{-3} T^0]$Equating dimensions on both sides:$[M^0 L^0 T^1] = [M L^0 T^{-2}]^x [L]^y [M L^{-3} T^0]^z$$[M^0 L^0 T^1] = [M^{x+z} L^{y-3z} T^{-2x}]$Comparing powers:For $M$: $x + z = 0 \Rightarrow z = -x$For $T$: $-2x = 1 \Rightarrow x = -1/2$Therefore,$z = 1/2$For $L$: $y - 3z = 0 \Rightarrow y = 3z = 3(1/2) = 3/2$Substituting these values back into the expression:$T = k S^{-1/2} r^{3/2} \rho^{1/2} = k \sqrt{\frac{\rho r^3}{S}}$

If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$,radius $(r)$ of the drop,and density $(\rho)$ of the liquid,then the expression for $T$ is:

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