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Entrance Exam Dates for 2020 and other related important dates for MH-CET, JEE, BITSAT, VIIT and many other
Almost all entrance exam dates are declared for Yr. 2020. Bellow are all dates tabulated in single table for user reference. including Application dates, result dates.
MH-CET, Joint Entrance, BITSAT VITEEand many more. exam dates and other important dates are here bellow
This is taken from respective websites and can be use as reference only for preparation. Please check with respective websites for any further change.
MH-CET, Joint Entrance, BITSAT VITEEand many more. exam dates and other important dates are here bellow
This is taken from respective websites and can be use as reference only for preparation. Please check with respective websites for any further change.
Water is filled in a rectangular tank of size 3m x 2m x 1 m. Find the total force exerted by the water on the bottom surface of the tank.
Question :
Water is filled in a rectangular tank of size 3m x 2m x 1 m.
(a) Find the total force exerted by the water on the bottom surface of the tank.
(b) Consider a vertical side of area 2 m x 1 m. Take a horizontal strip of width ox metre in this side, situated at a depth of x metre from the surface of water. Find the force by the water on this strip.
(c) Find the torque of the force calculated in part (d) about the bottom edge of this side.
(d) Find the total force by the water on this side.
(e) Find the total torque by the water on the side about the bottom edge.
Neglect the atmospheric pressure and take g = 10 m/s2.
Answer :
Water is filled in a rectangular tank of size 3m x 2m x 1 m.
(a) Find the total force exerted by the water on the bottom surface of the tank.
(b) Consider a vertical side of area 2 m x 1 m. Take a horizontal strip of width ox metre in this side, situated at a depth of x metre from the surface of water. Find the force by the water on this strip.
(c) Find the torque of the force calculated in part (d) about the bottom edge of this side.
(d) Find the total force by the water on this side.
(e) Find the total torque by the water on the side about the bottom edge.
Neglect the atmospheric pressure and take g = 10 m/s2.
Answer :
( a) Given dimensions of the
tank ,
Length (L) = 3 m,
Breadth (B) = 2 m,
Height (H) = 1 m.
As tank is filled, the height of water in the tank = H =
1 m.
The pressure of water at the bottom
= ρgH
=1000*10*1
=10000 N/m²
Area of the bottom of the tank = L x B
= 3 m x 2 m
=
6 m²
So the force on the bottom = Pressure * Area
=10000*6
= 60000 N
(b)
The pressure at x m below the surface of the water = ρgx
Area
of a horizontal strip ẟx wide and 2 m length =2*ẟx
The force on this strip F =Area*pressure
=2*
ẟx*ρgx
=2*ẟx*1000*10*x
=20000.x.ẟx
N
(c)
The perpendicular distance of this force from the bottom of edge of this side =
H-x =1-x m
Hence, the torque of the force = Force*perpendicular
distance
=20000.x.ẟx*(1-x) N-m
=20000.x(1-x)ẟx
N-m
(d)
The total force of the water on this side =∫Fda,
{from x=0 to x=1 m,
where
F is the pressure at the depth x m and da=area of the strip}
=∫ρgx*(2*dx)
{dx is the width of the strip}
=2ρg∫x.dx =2ρg*[x²/2] {Limit from x=0 to
x=H=1 m} =ρgH²
=1000*10*1²
=10000 N
(e)
The variation of the pressure will be triangular as shown in the figure.
We can also find out the force on the side of the tank by calculating the area
of this triangle.
Total Force =½*ρgH*H*(2 m)
=ρgH²
=1000*10*1²
=10000 N The height of this resultant force from the bottom of edge of
the side will be one-third of H (height of the C.G. from the bottom) =H/3
Hence the torque =10000*H/3
=10000*1/3 N-m
=10000/3 N-m
We are part of nature …..not apart from it.
1.
We are part of
nature …..not apart from it.
‘One of
the conditions of happiness is that the link between man and nature shall not
be broken.’
Just living is not enough …..one must have sunshine
,freedom, and a little flower. Nature – the creator, the parent. She happens to
be called by us as mother. We may claim ourselves as a creature who negligibly
dependent on this mother of ours.
In his haste
to acquire space for living and business,
man very often forget that he is a part of environment. The environment
is very important in human existence as it is basically all that surround us.
The human life basically depends upon healthy produce and the balanced
environmental conditions. The
environment however could affect
humans physically ,spiritually and culturally. Humen are known to solely depend
on earth’s resources such as : oil, forest, water, energy and others. These
resources however get limited in time and human are known to largely consume
them.
We
often build houses ,factories and dams without any concern for environment. He
cuts down trees mercilessly and destroys nature. When all the trees have been
cut down,when all the animals have been hunted, when all the waters are
polluted, when all the air is unsafe to breathe, only then we will discover
that we can’t eat money.
Nature and Human have a symbiotic relationship.Human affect the nature
by polluting and nature affects human beings by increased level of global warming, cloudburst etc. So it is the
duty of every human being to ensure that we protect our nature.
A thing of beauty is joy for ever
1. A thing of beauty is
joy for ever
It implies the fact that a
true beauty is eternal. Once a person has experienced beauty, he/she carry the
joy of that experience within them for the rest of their lives. True beauty is timeless.
Try and seek beauty in everyday life really brings a superficial joy forever. This
phrase has been able to provide us a link between abstract and concrete notion
of beauty.
A real beauty
of an object or idea not only lasts forever but also increases its aesthetic
beauty as the years progress. John Keats says that “truth is beauty and beauty
is truth.” It is true to say that actual beauty of anything provides
us a deep truths about life.
Life presents us many beautiful things. This may be a
beautiful scene or a flower or a lonely night walk on a beach that fill us with peace of a
beautiful picture. We should store these pretty memories in our sub-conscious
mind. When we are not feeling so good , or are lonely or depressed ,we should remember the
beautiful sights that we have
experienced . This will make us happy.
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