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**A metal cube of edge 5cm and density 9.0 gcm-3 is suspended by a thread so as to be completely immersed in a liquid of density 1.2 cm-3. Find the tension in the thread.**

**(Take g = 10 m/s2)**

**[Hint: Tension in thread = apparent weight of the cube in liquid**

Answer:

Given:

Density of metal cube = 9.0 gcm-3

Density of liquid = 1.2 gcm-3

Side of the cube = 5cm

Volume of the cube = 5 x 5 x 5 = 125cm3

To find the weight of the cube:

Mass of the cube = volume of the cube x density of the cube

= 125 x 9 = 1125 g

∴ Weight of the cube = 1125 gf

The weight of the cube acts downwards

Upthrust acting on the cube = weight of the liquid moved

= volume of the cube x density of the liquid x g

= 125 x 1.2 x g = 150gf

Upthrust on the cube acts in the upward direction

Tension in thread = total force acting in the downward direction

= weight of the cube acting downwards – upthrust acting on the cube

= 1125 – 150 = 975gf or 9.75N

"hello everyone welcome to vidu
this is priya and here we have an
interesting question to solve
let us look into the question a metal
cube
of edge 5 centimeter and density
9 gram per centimeter cube
is suspended by a thread
as to be completely immersed in a liquid
of
density 1.2 centimeter
cube find the tension in the thread
take gravity equal to 10 meter per
second square so what's a hint given
here
is tension in thread equal to apparent
weight of the cube in liquid
so let us see what are the
values given the question
it has given the value of
density of the metal cube which
is 9.0 gram per
centimeter cube and it has also given
the density
of liquid which is 1.2
gram per centimeter cube
and the side the side of the cube
also given and
we need to find out the volume of the
cube
we have a formula volume
of q
equal to
5 into 5
into 5 which is
1 25
centimeter
cube so which gives a value of
125 centimeter cube and
to find the weight of the cube we have a
formula
mass of
the q
equal to volume of the queue
volume of q
into density of the q
we know mass of the cube equal to volume
of the cube into
density of the cube
and when we substitute the value 125
in volume of the cube and we know the
density of the cube which is
9 when we multiply these two
120
1 25
into nine which gives
one thousand
one hundred and twenty
five grams so
this is the weight of the cube
the weight of the cube acts downwards
the weight of the cube acts downwards
so up thrust
acting
on the queue
equal to weight of liquid
weight of liquid
you want
as we know abstract acting on the cube
equal to weight of the liquid
which has spelled our mode that implies
volume of the cube
into
density of the liquid
density of the
liquid
into gravity so we know volume of the
cube
is 125
and density of the liquid is 1.2
and we know the gravity is
10 which gives an answer
1 50
g f
a thrust on the on the cube acts in the
upward direction this is for
downward direction and when we see the
uprest of the cube on upward direction
let us see
a thrust
off the cube
acting
in the upward direction
if it is a upward direction
tension in thread
tension in
thread
equal to total force
total force
acting
in the
downward direction
so tension in thread is a total force
acting in the
downward direction so we need to measure
weight of the cube
weight of the cube
acting downwards
minus upthrust
acting on the cube
so to find out the tension
in the thread we know total force acting
in the cube
downward direction will be will be the
tension in thread
so we get this
by taking weight of the cube acting
downwards minus up thrust acting on the
cube
we know the weight of the cube is
1125
and we know the upthrust acting on the
cube
which is 150 so total will get
975
g f or we can also write this as
9.75 newton
hope you understand this video if you
like my video please subscribe to our
channel and if you have any doubts you
can keep a message in comment box thank
you"

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