Two cylindrical vessels of equal cross-sectional area $16\,cm ^{2}$ contain water upto herghts $100\,cm$ and $150\,cm$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is $......J$ [Take density of water $=10^{3}\,kg / m ^{3}$ and $g =10\,ms ^{-2}$ ]
A$0.25$
B$1$
C$8$
D$12$
JEE MAIN 2022, Diffcult
Download our app for free and get started
B$1$
b $h =\frac{ h _{1}+ h _{2}}{2}$
Now,
$W = U _{1}- U _{f}$
$W =\left(\rho A h_{1}\right) g \frac{h_{1}}{2}+\left(\rho A h_{2}\right) g \frac{h_{2}}{2}-\rho A \left( h _{1}+h_{2}\right) g$
$\left(\frac{h_{1}+h_{2}}{4}\right)$
$W =\frac{\rho Ag }{2}\left[ h _{1}^{2}+ h _{2}^{2}-\frac{\left( h _{1}+ h _{2}\right)^{2}}{2}\right]$
$W =1\,J$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}\ m $ The water velocity as it leaves the tap is $0.4$ $ms^{-1}$ છે. The diameter of the water stream at a distance $2 \times 10^{-1}$ $m$ below the tap is close to .......$\times 10^{-3}\;m$
A $U-$tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with $10.0\; cm$ of water in one arm and $12.5\; cm $ of spirit in the other. if $15.0\; cm$ of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels (in $cm$) of mercury in the two arms?
A spring balance reads $200 \,gF$ when carrying a lump of lead in air. If the lead is now immersed with half of its volume in brine solution, what will be the new reading of the spring balance? specific gravity of lead and brine are $11.4$ and $1.1$ respectively ........... $gF$
A thin tube sealed at both ends is $100\, cm$ long. It lies horizontally, the middle $20\, cm$ containing mercury and two equal ends containing air at standard atmospheric pressure . If the tube is now turned to a vertical position, by what amount will the mercury be displaced ? (Given : cross-section of the tube can be assumed to be uniform) ........ $cm$
Spherical balls of radius $ 'r'$ are falling in a viscous fluid of viscosity '$\eta$' with a velocity $ 'v'. $ The retarding viscous force acting on the spherical ball is
A square gate of size $1\,m \times 1\,m$ is hinged at its mid-point. A fluid of density $\rho$ fills the space to the left of the gate. The force F required to hold the gate stationary is