If energy (E), velcocity (V) and time (T) were chosen as fundamental physical quantities for measurement, then the dimensional formula for mass will be

Options

A. `[E^(1) V^(2)T^(1)]`
B. `[E^(2)V^(-2)T^(0)]`
C. `[E^(1)V^(-2)T^(0)]`
D. `[E^(-1)V^(2)T^(1)]`

Explanation

To find the dimensional formula for mass (m) in terms of energy (E), velocity (V), and time (T), we can start by using the relationship between kinetic energy and mass.

### Step-by-Step Solution:

1. **Understand the relationship between kinetic energy and mass**:
The formula for kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} mv^2 \]
where \(m\) is mass and \(v\) is velocity.

2. **Express kinetic energy in terms of mass**:
Rearranging the equation for kinetic energy, we can express mass as:
\[ m = \frac{KE}{\frac{1}{2} v^2} = \frac{2 \cdot KE}{v^2} \]

3. **Substitute the dimensional formula for energy**:
The dimensional formula for energy (E) is:
\[ [E] = [M][L^2][T^{-2}] \]
where \([M]\) is mass, \([L]\) is length, and \([T]\) is time.

4. **Substitute the dimensional formula for velocity**:
The dimensional formula for velocity (V) is:
\[ [V] = [L][T^{-1}] \]

5. **Substitute the dimensional formula for mass**:
Now, substituting the dimensional formulas into our expression for mass:
\[ m = \frac{2E}{V^2} \]
Thus, the dimensional formula for mass becomes:
\[ [m] = \frac{[E]}{[V^2]} = \frac{[M][L^2][T^{-2}]}{[L^2][T^{-2}]} \]

6. **Simplify the expression**:
When we simplify this, we find:
\[ [m] = [M] \]
Thus, the dimensional formula for mass in terms of energy and velocity is:
\[ [m] = [E][V^{-2}][T^0] \]

### Final Answer:
The dimensional formula for mass (m) in terms of energy (E), velocity (V), and time (T) is:
\[ [m] = [E][V^{-2}] \]