Question

A block weights $5N$ in air, $4.5N$ in a liquid of specific gravity $0.5$. Its weight in water will be
(A) $3.5N$
(B) $4.0N$
(C) $2.5N$
(D) $3.0N$

Answer 1

The weight of a body is the product of mass and the acceleration due to gravity. We need to relate specific gravity to volume and weight to solve the question, and then we can find the answer.

Complete Step by Step Solution: Specific Gravity gives information about the weight and density of the object. It can be calculated by comparing the weight, mass and density of the given object with water of the same amount at ${4^ \circ }C$. Specific gravity is a dimensionless measurement.
Specific gravity of a substance is given by,
${\text{Specific Gravity = }}\dfrac{{{\text{Mass of unit volume of the substance}}}}{{{\text{Mass of unit volume of water}}}}$.
It is basically the ratio of density of the substance to the density of some standard substance at a specific temperature. This also means in the case of liquid, the density of any substance (fluid) divided by the density of water will give the specific gravity.
It has been given that, in a liquid of specific gravity $0.5$, the weight of a solid is $4.5N$.
The weight of the same solid in air is $5N$. Thus, $mg = 5N$ where $m$ is the mass and $g$ is the acceleration due to gravity.
In a liquid of specific gravity $0.5$. Thus, $\sigma = 0.5$.
Thus, we can write,
$mg - \sigma Vg = 4.5$
$\Rightarrow 5 - 0.5Vg = 4.5$
Simplifying the equation further, $0.5Vg = 0.5$
Thus, the volume is given by, ${\text{V = 0}}{\text{.1}}{{\text{m}}^{\text{3}}}{\text{.}}$
In water,
$mg - \sigma Vg = 5 - 0.5 \times 0.1 \times 10$
$= 5 - 1 = 4N$

Hence, the correct answer is Option B.

Note: Specific gravity is a parameter which tells us about the relative weight of the material with respect to the same amount of water. Specific gravity of the liquid is given by the ratio of weight loss of the solid in liquid to weight loss of the solid in water.
If the specific gravity of a body is greater than 1, then it will sink in water and if it is less than 1, then the body will float in water. If the specific gravity has a value equal to 1, then the body will neither sink nor float.
There are a lots of applications based on specific gravity one of these are:
For example: Urine test can be done by Osmolality (it is a more specific test for urine concentration) as well as specific gravity, but specific gravity is easiest and more convenient. This test shows concentration of all chemical particles in urine. It is determined by the solutes (ions such as ammonium) in urine. The less solutes, the lower the specific gravity.