If force `(F)`, velocity `(V)` and time `(T)` are taken as fundamental units, then the dimensions of mass are
(a)`[FvT^(-1)]` (b)`[FvT^(-2)]` (c)`[Fv^(-1)T^(-1)]` (d)`[Fv^(-1)T]`

Options

A. `[FvT^(-1)]`
B. `[FvT^(-2)]`
C. `[Fv^(-1)T^(-1)]`
D. `[Fv^(-1)T]`

Explanation

To find the dimensions of mass when force (F), velocity (V), and time (T) are taken as fundamental units, we can follow these steps:

### Step 1: Write the formula for force
The formula for force (F) is given by Newton's second law of motion:
\[ F = m \cdot a \]
where \( m \) is mass and \( a \) is acceleration.

### Step 2: Express acceleration in terms of velocity and time
Acceleration (a) can be expressed as the change in velocity over time:
\[ a = \frac{\Delta V}{\Delta T} \]
For our purposes, we can simplify this to:
\[ a = \frac{V}{T} \]
where \( V \) is velocity and \( T \) is time.

### Step 3: Substitute acceleration back into the force equation
Now, substituting the expression for acceleration back into the force equation gives us:
\[ F = m \cdot \frac{V}{T} \]

### Step 4: Rearrange to solve for mass
To find the mass (m), we rearrange the equation:
\[ m = \frac{F \cdot T}{V} \]

### Step 5: Write the dimensions of mass in terms of F, V, and T
Now we can express the dimensions of mass in terms of the fundamental units of force (F), velocity (V), and time (T):
\[ [m] = [F] \cdot [T] \cdot [V]^{-1} \]
This gives us:
\[ [m] = [F]^{1} \cdot [V]^{-1} \cdot [T]^{1} \]

### Step 6: Finalize the dimensions of mass
Thus, the dimensions of mass can be expressed as:
\[ [m] = [Fv^{-1}T] \]
This corresponds to option (d).

### Conclusion
The dimensions of mass when force, velocity, and time are taken as fundamental units is:
\[ [m] = [Fv^{-1}T] \]