**Introduction**

In this Science Experiment, we will learn to determine the density of solid by using a spring balance and a measuring cylinder.

**Density**

Below are some points for a quick revision of density.

- Density is the physical property of matter that describes the maximum number of molecules collected.
- Density is also described as mass per unit volume, i.e.,

**Density= Mass/Volume**

- It is directly proportional to the mass of the matter. Greater the mass maximum will be the density.
- The matter with the maximum density sinks into the water while the matter with the lesser density floats onto it.
- It is inversely proportional to the volume, i.e., if two matters have the same mass but two different volumes, then the matter having lesser volume will have greater density.
- Kg/m^3 is the SI unit of density.
- Density of a substance is inversely proportional to temperature, i.e., the more the temperature, the lesser the density.

**The density of some substances in Kg/m^3 are:-**

**Iron = 7800 **

**Ice = 920**

**Water at 20℃ = 998**

**Water at 4℃ = 1000**

**Air = 1.30**

** **

**Examples**

1. Flotation of oil on water.

2. Sinking of iron into the water.

3. Flotation of cotton on water.

**Relative Density**

** 1. **The relative density of an object is equal to the ratio of the density of the substance and the density of water, i.e.,

**Relative Density = Density of an object/ Density of water at 4℃.**

2. Relative density is the unit-less quantity.

3. If the relative density of a substance is less than 1, then it will float on water. If the relative density of a substance is greater than 1, then it will sink in water.

**Spring Balance**

**1. **It is an object whose one end is attached to any fixed or heavy surface, and another end is attached with a hook to hold any other thing.

2. It works on the principle of elasticity.

3. The stretched length is directly proportional to the force applied to stretch it.

**F ****∝**** x, **where x is stretched length.

**F = -kx, **where k represents the spring constant.

4. Negative sign indicates that the force applied and length stretched both are in opposite directions.**
**5. The force applied by the object on spring is balanced by the force of gravity, i.e., F=mg. Through this, we can measure the weight of the object.

6. It is used for measuring heavy loads.

7. Spring balance is used in the laboratory for experiments.

**Aim**

To determine the density of solid by using a spring balance and a measuring cylinder.** **

**Apparatus Required For The Experiment**

1. An object of metal,

2. Metallic cylinder,

3. Iron stand,

4. Spring balance.** **

**Theory**

**1. **Mass per unit volume is density, represented by ρ.

2. ⍴ = M/V,

Where M = Mass of object

V = Volume of object

3. Let the weight of the object measured by spring balance be W.

4. Let the volume of water be V1.

5. Let the volume of water when the object is immersed inside the water be V2.

Therefore, the volume of the object will be equal to the displaced volume, i.e., (V2-V1).

Then, Density=W/(V2-V1).

**Procedure**

**Step 1.** With the help of an iron stand, hang the spring in a vertical position. Note it’s reading W1.

**Step 2**. Measure the least count of spring balance by using the formula

Least Count = Range of given spring balance/ Total number of divisions.

**Step 3.** Check its zero error and record with a proper sign if there’s any.

**Step 4.** Hang the object with the hook of the spring balance.

**Step 5.** Note the reading when the object stops moving further W2

**Step 6.** Measure W2 – W1. This is the weight of the object.

**Step 7.** Measure the true weight of an object by subtracting it from zero error.

**Step 8.** Obtain its mean weight by repeating this process thrice.

**Measurement of volume of the object**

**Step 9.** Pour some water into the measuring cylinder and write down its initial level. Let its volume be V1

**Step 10.** Remove the object from a spring balance.

**Step 11.** Tie the object with a thin thread and immerse it in the measuring cylinder.

**Step 12.** Note the raised water. Let it be V2.

**Step 13.** Measure the volume of the object by subtracting V1 from V2.

**Step 14.** Find its mean volume by repeating this experiment thrice.

**Observation **

Least Count of spring balance= ……..g wt

Zero error of spring balance = ……..g wt

Least count of measuring cylinder = ……..ml

**Table 1; Measurement of the weight of a given object**

S.NO. | Reading of spring balance without object W1 | Reading of spring balance with object W2 | Weight of object, W=W2-W1 | True weight W’= W- zero error |

1. | ||||

2. | ||||

3. |

Mean weight of the object = (W’1 + W’2 + W’3 )/3

= ……….. g wt

Mass of the given object M = ……….. g

**Table 2; Measurement of Volume of a given object.**

S.No | Volume of the water without object, V1 | Volume of the water when the object is immersed in it, V2 | Volume of object
V’= V2 -V1 |

1. | |||

2. | |||

3. |

Mean volume of the object = (V’1 + V’2 + V’3)/3

** = ………….. ml**

**Result**

Density of the given object = ( Mass/ Mean Volume) kg/m^3.

= ………………. kg/m^3

**Precaution**

1. Spring balance should be clean and error-free.

2. Spring balance must be hung vertically through an iron rod

3. Take the reading only after the object stops oscillating.

4. Measure the zero error accurately.

5. While immersing the object inside the measuring cylinder, keep in mind that the water should not fall out of it.

**Sources Of Error**

1. Spring could be permanently stretched.

2. Solid objects may absorb the water.

3. Least count of spring balance can be more.

**Viva Questions With Answer**

**Q.1 What is the SI unit of density?
**Ans. kg/m^3

**Q.2 What is the effect of temperature on density?
**Ans. Temperature is inversely proportional to density.

**Q.3 Give a difference between mass and weight.
**Ans Mass is a universal constant, while weight depends on gravity and changes with respect to it.

**Q.4 What is the value of g?
**Ans 9.8 m/sec

**Q.5 Relative density of silver is 10.8, and the density of water is 1000 kg/m^3. Calculate the density of silver.
**Ans. Relative density of silver= Density of silver/ Density of water

10.8= x/1000

x = 10.8 X 1000

= 10800 kg/m^3.

**Q.6 Whose density is greater. 1 kg of cotton or 1 Kg of iron?
**Ans. The density of 1 kg of iron is greater because it has less volume as compared to 1 kg of cotton.

**Q.7 What is the relation of density with volume?
**Ans. Density is inversely proportional to volume.

An Indian physicist and astronomer.

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