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(C) Let $A$ be the area of cross-section of the hole,$v$ be the initial velocity of efflux,and $d$ be the density of water.According to Torricelli's l

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Decrease of $12.5 \ gm-wt$

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(C) Let $A$ be the area of cross-section of the hole,$v$ be the initial velocity of efflux,and $d$ be the density of water.According to Torricelli's law,the velocity of efflux is $v = \sqrt{2gh}$.The volume of water flowing out per second is $V = Av$.The mass of water flowing out per second is $m = Avd$.The rate of change of momentum (thrust force) is $F = \frac{dp}{dt} = (Avd)v = Adv^2$.This thrust force acts upwards on the cylinder due to the reaction of the water jet.Substituting $v^2 = 2gh$,the upward reaction force is $F = Ad(2gh) = 2Adgh$.Given $A = \frac{1}{4} \ cm^2$,$d = 1 \ g/cm^3$,$g = 980 \ cm/s^2$,and $h = 25 \ cm$.$F = 2 	imes \frac{1}{4} 	imes 1 	imes 980 	imes 25 = 12250 \ dynes$.Since $1 \ gm-wt = 980 \ dynes$,the force in $gm-wt$ is $F = \frac{12250}{980} = 12.5 \ gm-wt$.As this force acts upwards,it causes a decrease in the effective weight of the cylinder on the balance.

$A$ cylinder containing water up to a height of $25 \ cm$ has a hole of cross-section $\frac{1}{4} \ cm^2$ in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?

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