To find the density of the cube, we first need to determine its volume using the measurements provided, and then we can calculate the density using the formula: density = mass/volume. Let's break this down step by step.
Step 1: Understanding the Measurements
From the problem, we know that:
- 9 divisions on the main scale are equal to 10 divisions on the vernier scale.
- 1 main scale division (MSD) is equal to 1 mm.
- The main scale reading (MSR) is 1 mm.
- 1 division of the vernier scale (VSD) coincides with the main scale.
Calculating the Least Count
The least count (LC) of the vernier calipers can be calculated using the formula:
LC = (Value of 1 MSD) - (Value of 1 VSD)
Since 9 MSD = 10 VSD, we can find the value of one VSD:
Value of 1 VSD = (9 MSD) / 10 = 0.9 mm
Now, substituting into the least count formula:
LC = 1 mm - 0.9 mm = 0.1 mm
Step 2: Finding the Total Measurement
Now, we can find the total reading of the cube's edge:
Total Reading = MSR + VSD = 1 mm + 0.9 mm = 1.9 mm
Converting to Centimeters
Since we need the volume in cubic centimeters, we convert the edge length from millimeters to centimeters:
1.9 mm = 1.9 / 10 = 0.19 cm
Step 3: Calculating the Volume of the Cube
The volume (V) of a cube is calculated using the formula:
V = edge length³
Substituting the edge length:
V = (0.19 cm)³ = 0.19 cm × 0.19 cm × 0.19 cm = 0.006859 cm³
Step 4: Calculating the Density
Now that we have the mass of the cube (2.736 g) and its volume (0.006859 cm³), we can calculate the density:
Density = Mass / Volume
Density = 2.736 g / 0.006859 cm³ ≈ 398.5 g/cm³
Significant Figures
When rounding to the correct significant figures, we observe that the mass (2.736 g) has four significant figures, while the volume (0.006859 cm³) has five significant figures. Therefore, we should express the density to four significant figures:
Density ≈ 398.5 g/cm³
Final Result
The density of the cube is approximately 398.5 g/cm³.
