Question

Calculate the up-thrust acting on a ball of volume $0.2{m^3}$ immersed in a liquid having density $1\dfrac{{kg}}{{{m^3}}}$ .
(A) 0.2f
(B) 2f
(C) 0.2gf
(D) 2gf

Answer 1

Hint
Upthrust, according to its definition, is equal to force acting on the body. So we get a formula of upthrust using this concept. After that we will use the formula of volume and find the mass volume density relation.
Then we will put this relation in the upthrust equation and equate it to find the up-thrust acting on a ball and then we will choose the correct option.

Complete step by step answer
Upthrust is the force exerted by a fluid on an object in upwards direction. That's why up-thrust acts against the weight of an object.
We know that Upthrust (U) = weight of the liquid displaced by the submerged part of the body.
So $U = mg$ , where m is mass of the body and g is the acceleration due to gravity.
We also know that volume $V = \dfrac{m}{D}$ , Where D is the density of the body.
So, we get $m = V \times D$ , now we put this equation into the upthrust equation.
Hence $U = mg = V \times D \times g$ .
Since volume of solid immersed in liquid is equal to the volume of the liquid displaced,
We get, upthrust = volume of solid immersed x density of liquid displaced x Acceleration due to gravity upthrust,
So, we get upthrust $U = V \times D \times g = 0.2{m^3} \times 1\dfrac{{kg}}{{{m^3}}} \times g = 0.2gf$.
So, the correct option is (C).

Note
The main concept of buoyancy force or upthrust force is if the object is less dense than the liquid, buoyancy will make it float and the volume of the object immersed in liquid is equal to the volume of the liquid displaced.