Q. A cylinder containing water upto a height of $25\ cm$ has a hole of cross-section $1/4\ cm^{2}$ in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out
A) Increase of $12.5\ gm$-$wt$
B) Increase of $6.25\ gm$-$wt$
C) Decrease of $12.5\ gm$-$wt$
D) Decrease of $6.25\ gm$-$wt$
Explanation
(c) Let $A =$ The area of cross section of the hole
$v =$ Initial velocity of efflux
$d =$ Density of water
Initial volume of water flowing out per second $= Av$
Initial mass of water flowing out per second $= Avd$
Rate of change of momentum $= Adv^{2}$
Initial downward force on the flowing out water $= Adv^{2}$
So equal amount of reaction acts upwards on the cylinder
$\therefore$ Initial upward reaction $= Adv^{2}$ [As $v = \sqrt{2gh}$]
$\therefore$ Initial decrease in weight $= Ad(2gh)$
$= 2Adgh = 2 \times \left( \frac{1}{4} \right) \times 1 \times 980 \times 25 = 12.5\ gm$-$wt$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.