A $20 \,cm$ long tube is closed at one end. It is held vertically, and its open end is dipped in water until only half of it is outside the water surface. Consequently, water rises in it by height $h$ as shown in the figure. The value of $h$ is closest to .............. $\,m / s$ (assume that the temperature remains constant, $P _{\text {armosphere }}=10^5 \,N / m ^2$, density. of water $=10^3 \,kg / m ^3$, and acceleration due to gravity $g =10 \,m / s ^2$ )
KVPY 2021, Advanced
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