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A cylinder of radius R is kept embedded along the wall of a dam as shown. Take density of water as #rho#. Take length as L. The force exerted by liquid on the cylinder in horizontal direction is [Neglecting atmospheric pressure]?

A) #2R^(2)rhogL#
B) #R^(2)rhogL#
C) #4R^(2)rhogL#
D) #1.61R^(2)rhogL#

Answer 1

Amelia Adams

Average horizontal pressure on the surface of cylinder

#P_"ave"=rhogh_C# where #h_C# is depth of centroid (midpoint) of the surface

Inserting value of #h_C# from the figure

#P_"ave"=rhog(R+R)=2Rrhog#

Area of the cylinder exposed to pressure#=2RxxL#

Now #"Force"="Pressure"xx"Area"#

#:."Force"=2Rrhogxx2RL=4R^2rhogL#

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Answer 2

Isabella Alvarez

The force exerted by the liquid on the cylinder in the horizontal direction is zero.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

A cylinder of radius R is kept embedded along the wall of a dam as shown. Take density of water as #rho#. Take length as L. The force exerted by liquid on the cylinder in horizontal direction is [Neglecting atmospheric pressure]?

A) #2R^(2)rhogL# B) #R^(2)rhogL# C) #4R^(2)rhogL# D) #1.61R^(2)rhogL#

A) #2R^(2)rhogL#
B) #R^(2)rhogL#
C) #4R^(2)rhogL#
D) #1.61R^(2)rhogL#