If 'm' is mass 'Q' is charge and B is magnetic induction, m//BQ has the same dimensions as

Options

A. Frequency
B. `("Frequency")^(-1)`
C. Velocity
D. Acceleration

Answer

To solve the problem, we need to determine the dimensions of the expression \(\frac{m}{BQ}\), where \(m\) is mass, \(Q\) is charge, and \(B\) is magnetic induction.

### Step 1: Write down the dimensions of each quantity
- The dimension of mass \(m\) is \([M]\).
- The dimension of charge \(Q\) is \([I \cdot T]\) (where \(I\) is current and \(T\) is time).
- The dimension of magnetic induction \(B\) is \([M \cdot T^{-2} \cdot I^{-1}]\).

### Step 2: Substitute the dimensions into the expression
Now, we can substitute these dimensions into the expression \(\frac{m}{BQ}\):
\[ \frac{m}{BQ} = \frac{[M]}{[M \cdot T^{-2} \cdot I^{-1}] \cdot [I \cdot T]} \]

### Step 3: Simplify the expression
Now, let's simplify the denominator:
\[ BQ = [M \cdot T^{-2} \cdot I^{-1}] \cdot [I \cdot T] = [M \cdot T^{-1}] \]
Thus, we have:
\[ \frac{m}{BQ} = \frac{[M]}{[M \cdot T^{-1}]} = [T] \]

### Step 4: Conclusion
The dimensions of \(\frac{m}{BQ}\) simplify to \([T]\), which represents time.

### Final Answer
The expression \(\frac{m}{BQ}\) has the same dimensions as time \([T]\).