Which of the following relations is dimensionally incorrect?

Options

A. `1u=931.5` MeV
B. 1u=931.5 MeV`//c^(2)`
C. 1u=1.67`xx10^(-27)kg`
D. none of these

Explanation

To determine which of the given relations is dimensionally incorrect, we need to analyze each option based on their dimensions. Let's go through the steps systematically.

### Step 1: Understand the Dimensions
We need to know the dimensions of the quantities involved:
- Energy (E) has the dimension of \([M L^2 T^{-2}]\).
- Mass (m) has the dimension of \([M]\).
- The speed of light (c) has the dimension of \([L T^{-1}]\).

### Step 2: Analyze Each Option
Let's analyze the options one by one:

1. **Option 1: \(1 \, u = 931.5 \, MeV/c^2\)**
- Here, \(MeV\) is a unit of energy.
- The right side can be expressed as:
\[ \frac{MeV}{c^2} = \frac{[M L^2 T^{-2}]}{[L^2 T^{-2}]} = [M] \]
- Thus, this equation is dimensionally correct.

2. **Option 2: \(1 \, u = 931.5 \, MeV\)**
- The right side is simply energy.
- The dimensions here are:
\[ [M L^2 T^{-2}] \]
- Since the left side represents mass, this equation is dimensionally incorrect.

3. **Option 3: \(1 \, u = 1.67 \times 10^{-27} \, kg\)**
- The right side is in kilograms, which is a unit of mass.
- Thus, this equation is dimensionally correct.

### Step 3: Conclusion
From the analysis above, we can conclude that:
- **Option 1** and **Option 3** are dimensionally correct.
- **Option 2** is dimensionally incorrect.

Therefore, the answer to the question is that the relation \(1 \, u = 931.5 \, MeV\) is dimensionally incorrect.