Question

In a sedimentary rock, the diameters of two grains A and B are 1ϕ and 3ϕ, respectively. The difference in diameters between A and B is_________mm (rounded off to two decimal places).

Hint:

The \(\varphi\) scale is used to express grain sizes in sedimentology. A lower \(\varphi\) value corresponds to larger grain sizes.

Answer 1

Correct Answer: 0.37

Step 1: Understanding the \(\varphi\) Scale.
The \(\varphi\) scale is a logarithmic scale used to describe the size of sedimentary grains. The relationship between the \(\varphi\) scale and the grain size in millimeters is: \[ \text{Grain Size (mm)} = 2^{\varphi}. \] For grain A with 1ϕ: \[ \text{Grain Size of A} = 2^1 = 2 \, \text{mm}. \] For grain B with 3ϕ: \[ \text{Grain Size of B} = 2^3 = 8 \, \text{mm}. \] Step 2: Calculate the Difference in Diameter.
The difference in diameters is: \[ \text{Difference} = 8 - 2 = 6 \, \text{mm}. \] Step 3: Conclusion.
The difference in diameters between grain A and grain B is 0.8 mm when using the \(\varphi\) scale.