The physical quantity which has dimensional formula as that of `("Energy")/("mass" xx "length")` is

Options

A. Force
B. Power
C. Pressure
D. Acceleration

Answer

To solve the problem, we need to find a physical quantity that has the same dimensional formula as \( \frac{\text{Energy}}{\text{Mass} \times \text{Length}} \).

### Step 1: Write down the dimensional formula for energy.
The dimensional formula for energy (E) is given by:
\[ [E] = [M][L^2][T^{-2}] \]
where \( M \) is mass, \( L \) is length, and \( T \) is time.

### Step 2: Write down the dimensional formula for mass and length.
The dimensional formulas for mass (M) and length (L) are:
\[ [M] = [M] \]
\[ [L] = [L] \]

### Step 3: Substitute the dimensional formulas into the expression.
We need to evaluate:
\[ \frac{[E]}{[M] \times [L]} = \frac{[M][L^2][T^{-2}]}{[M] \times [L]} \]

### Step 4: Simplify the expression.
When we simplify the expression, the mass (M) in the numerator and denominator cancels out:
\[ = \frac{[L^2][T^{-2}]}{[L]} = [L][T^{-2}] \]

### Step 5: Interpret the result.
The simplified dimensional formula \( [L][T^{-2}] \) corresponds to acceleration (A), which is defined as the change in velocity per unit time.

### Conclusion:
Thus, the physical quantity which has the dimensional formula as \( \frac{\text{Energy}}{\text{Mass} \times \text{Length}} \) is acceleration.

**Final Answer: Acceleration (A)**

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