Answer

Verified

18.6k+ views

**Hint:**When a body is partially or completely immersed in a fluid, a force acts on it in the upward direction which is called force of buoyancy or buoyant force. It is given by ${F_B} = \sigma \times V \times g$ where $\sigma $ is the density of the body, $V$ is the volume of the body in consideration and $g$ is the acceleration due to gravity.

Due to this buoyant force, the body loses some of its weight which is equal to the weight of the fluid displaced by the immersed part of the body.

**Complete step by step answer**

As given in the question, the ice is partially immersed in water.

We know that when a body is partially or completely immersed in a fluid, a force acts on it in the upward direction which is called force of buoyancy or buoyant force. It is given by ${F_B} = \sigma \times V \times g$ where $\sigma $ is the density of the body, $V$ is the volume of the body in consideration and $g$ is the acceleration due to gravity.

And according to the Archimedes’ Principle, due to this buoyant force, the body loses some of its weight which is equal to the weight of the fluid displaced by the immersed part of the body.

Let $f$ be the fraction of volume of the ice that is inside the water. Then $\left( {1 - f} \right)$ will be the fraction of volume above water. We know that the density of water $\rho = 1000{\text{ kg/}}{{\text{m}}^3}$ and the density of ice is given $\sigma = 917{\text{ kg/}}{{\text{m}}^3}$ . Now, we apply Archimedes’ Principle to find the answer i.e.

${\text{Buoyant Force }} = {\text{ Displaced weight of water}}$

$\sigma \times \left( {1 - f} \right) \times V \times g = \rho \times f \times V \times g$

On substituting the value and simplifying we have

\[917 \times \left( {1 - f} \right) = 1000 \times f\]

On further solving we have

$f = 0.917$

Therefore, the fraction of volume of the ice above water is $\left( {1 - f} \right) = 1 - 0.917 = 0.083$

**Hence, option A is correct.**

**Note:**The Archimedes’ Principle has numerous important applications in our life. It is used in designing the ships, boats and other water bodies. They are also used in producing Hydrometers which are used to measure density of different liquids.

Recently Updated Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main

Find the points of intersection of the tangents at class 11 maths JEE_Main

For the two circles x2+y216 and x2+y22y0 there isare class 11 maths JEE_Main

The path difference between two waves for constructive class 11 physics JEE_MAIN

What is the difference between solvation and hydra class 11 chemistry JEE_Main

Other Pages

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

Derive an expression for maximum speed of a car on class 11 physics JEE_Main

Why does capacitor block DC and allow AC class 12 physics JEE_Main