Question

State the relationship of upthrust with the following.
Volume of the immersed part of the object
Density of the fluid​

Answer 1

Answer:

Upthrust is directly proportional to the density of the fluid and volume of the object. ... It states that a body either wholly or partially immersed in a fluid, experiences upthrust thereby appearing to lose weight which is equal to the weight of fluid displaced.

Answer 2

Answer:

Upthrust is directly proportional to the density of the fluid and volume of the object. ... It states that a body either wholly or partially immersed in a fluid, experiences upthrust thereby appearing to lose weight which is equal to the weight of fluid displaced

Explanation:

Upthrust:

A wood piece placed on water floats. It is because of the upward force exerted by water. The objects thus appear to lose weight.

The upward force exerted by a fluid on an object is called upthrust.

Upthrust is directly proportional to the density of the fluid and volume of the object.

Archimedes’ Principle:

It states that a body either wholly or partially immersed in a fluid, experiences upthrust thereby appearing to lose weight which is equal to the weight of fluid displaced.

Mathematically, Upthrust = Loss of weight = Weight of fluid displaced.

Numerical Problems:

1. A metal cube of edge 10 cm and density 8 gcm-3 is suspended by a thread in a liquid of density 1.5 gcm-3. Find the tension in the thread.

Sol:

Force acting = Apparent weight in liquid

= Wt. of metal – loss of weight.

Volume of cube = S3 = 1000 cm3.

Wt. of metal in air = V´ d ´ g = 1000 ´ 8 = 8000 gf

Volume of liquid displaced = Volume of object = 1000 cm3.

Weight of liquid displaced = v ´ d ´ g = 1000 ´ 1.5 = 1500 gf

Apparent wt. or tension = 8000 gf – 1500 gf = 6500 gf.

6.5 kgf or 65 N …[Whenever value of g is not given, it maybe taken as 10 Nkg-1]