Force acting on a particle is given by `F=(A-x)/(Bt)`, where x is in metre and t is in seconds. The dimensions of B is -

Options

A. `MLT^(-2)`
B. `M^(-1)T^(-3)`
C. `M^(-1)T`
D. `MT^(-1)`

Answer

To find the dimensions of \( B \) in the equation \( F = \frac{A - x}{Bt} \), we will follow these steps:

### Step 1: Identify the dimensions of force
The dimension of force \( F \) is given by:
\[ [F] = MLT^{-2} \]
where \( M \) is mass, \( L \) is length, and \( T \) is time.

### Step 2: Analyze the right-hand side of the equation
The right-hand side of the equation is \( \frac{A - x}{Bt} \). Since \( A \) and \( x \) are both lengths (in meters), their dimensions are:
\[ [A] = [x] = L \]
Thus, the dimension of \( A - x \) is also \( L \).

### Step 3: Write the dimensions for the right-hand side
Now, we can express the dimensions of the right-hand side:
\[ \frac{A - x}{Bt} = \frac{L}{[B][T]} \]
where \( [B] \) is the dimension of \( B \) and \( [T] \) is the dimension of time.

### Step 4: Set the dimensions equal
Since the dimensions of both sides of the equation must be equal, we have:
\[ MLT^{-2} = \frac{L}{[B][T]} \]

### Step 5: Rearrange to solve for \( [B] \)
Rearranging the equation gives:
\[ [B] = \frac{L}{MT^{-2} \cdot T} = \frac{L}{MT^{-1}} = \frac{L T}{M} \]

### Step 6: Express the dimensions of \( B \)
From the above expression, we can write:
\[ [B] = M^{-1} L T \]

### Final Answer
Thus, the dimensions of \( B \) are:
\[ [B] = M^{-1} L T \]